## Hydrogen Spectrum: Frequency and Wavelength Relation

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The hydrogen emission spectrum can be represented using spectral lines, which is one way to go. Another way is using wavelength to represent the lines. There’s a mathematical relation between the speed of light, frequency, and wavelength. But, this relation forms two different views of the spectrum, i.e., using frequency and wavelength.

Read on to understand the relationship between the speed of light (c), wavelength(), and frequency(f).

**c=λv**

Further rearranging the equation,

**λ=****c/****v o****r, v=****c/****λ**

The above equations indicate that wavelength and frequency are inversely related to each other.

**Read More:-**

Electron Spin | Aufbau Principle |

## Hydrogen Spectrum Wavelength

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Whenever a hydrogen atom absorbs a photon, the electron undergoes an energy level transition, for example, n=1, n=2. When a photon passes through a hydrogen atom, the electron transitions from a higher to a lower energy state, for example, n=3, n=2. The transmission of light happens during this transition from a higher to a lower level.

The spectrum comprises wavelengths that reflect the differences in the quantized energy levels. These energy levels exist due to the quantized energy levels of the atoms. For example, the line at 656 nm corresponds to the transition n=3 n=2.

**Read More:** **Quantum Theory of Light**

## Hydrogen Emission Spectrum Series

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The Hydrogen Emission Spectrum is divided into several spectral series, with wavelengths calculated using the Rydberg formula. These spectral lines are formed by electrons in an atom transitioning between two energy levels.

The Rydberg formula became crucial in the development of quantum mechanics because it categorized the series. In astronomical spectroscopy, spectral series help in identifying the presence of hydrogen and calculate red transitions.

The Balmer series is the component of the hydrogen emission spectrum. It is responsible for an electron's excitation from the second shell to any other shell. Other transitions have their series names as well. Below is a list of some of them:

Lyman series | Transition from the first shell to any other shell |

Balmer series | Transition from the second shell to any other shell |

Paschen series | Transition from the third shell to any other shell |

Bracket series | Transition from the fourth shell to any other shell |

Pfund series | Transition from the fifth shell to any other shell |

**Read More:****Franck Hertz Experiment**

## Hydrogen Spectrum Series Formula

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A large number of spectral lines are present in the hydrogen spectrum. However, in 1890, Rydberg gave a very simplified theoretical equation for the wavelength of these lines. The equation provides a calculation of the wavenumber v of the lines by the formula:

Here, R is a constant called the **Rydberg constant**, and its value is equivalent to **109677 **cm−1. Also, n_{1} and n_{2} are whole numbers and for a particular series, n_{1} is constant and n_{2} varies.

- For the Lyman series, n
_{1}=1, n_{2}=2,3,4........ - For the Balmer series, n
_{1}=2, n_{2}=3,4,5........ - For the Paschen series, n
_{1}=3, n_{2}=4,5,6........ - For the Brackett series, n
_{1}=4, n_{2}=5,6,7........ - For the Pfund series, n
_{1}=5, n_{2}=6,7,8........

For H-like particles, the formula is:

Where Z is the atomic number of the H-like particle.

**Read More About****Hund’s Rule of Maximum Multiplicity**

## Things To Remember

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- When an electron in a hydrogen atom goes from a higher energy level to a lower energy level, the difference in energies between the two levels is emitted as a specific wavelength of radiation. It's known as a spectral line.
- The hydrogen spectrum lines are:
**Lyman series, Balmer series, Paschen series, Brackett series, Pfund series**. - The infinity level indicates the maximum amount of energy that an electron can have as a component of a hydrogen atom. If the electron's energy reaches that threshold, it is no longer a part of the atom. The infinity level denotes the point at which the atom is ionised to create a positively charged ion.
- Hydrogenic (Hydrogen like) atoms consist of a nucleus with positive charge ‘+Ze’ and a single electron. Here ‘Z’ is atomic mass number and ‘e’ is the quantised unit of charge.

## Sample Questions

**Ques. What is the wavelength of the light emitted when the electron in a hydrogen atom undergoes transition from the energy level with n = 4 to energy level n = 2 ? What is the colour corresponding to this wavelength ? (Given RH = 109678 cm ^{-1}) (2 Marks)**

**Ans.** According to Balmer formula,

**Ques. Emission transitions in the Paschen series end at orbit n = 3 and start from orbit n and can be represented as v = 3.29 x 10**^{15}** (Hz) [1/3****2**** – 1 /n**^{2}**]. Calculate the value of n if the transition is observed at 1285 nm. Find the region of the spectrum. (3 Marks)**

The Paschen series lies in the infrared region of the spectrum.

**Ques. What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition n = 4 to n = 2 of He****+**** spectrum? (4 Marks)**

**Ans. **For He+ ion, the wave number (v) associated with the Balmer transition, n=4 to n=2 is given by:

By hit and trial method, the equality given by equation (1) is true only when n_{1}=1 and n_{2}=2.

∴The transition for n2=2 to n=1 in hydrogen spectrum would have the same wavelength as Balmer transition n=4 to n=2 of He^{+} spectrum.

**Ques. Name the series of hydrogen spectra which lies in the ultraviolet region. Give an explanation to support your answer. (5 Marks)**

**Ans. **The atomic hydrogen emits a line spectrum consisting of various series. In the hydrogen spectrum, the spacing between lines within certain sets of the hydrogen spectrum decreases in regular ways. Each of these sets are called spectral series. Balmer, Lyman, Paschen, brackett, and Pfund series are subsequently found in spectral series of the hydrogen spectrum at different wavelengths.

Lyman series:

1λ=R[112−1n_{2}],where,n=2,3,4...

The Lyman series is in the ultraviolet region.

According to third postulate of Bohr’s model, when an atom makes a transition from the higher energy state with quantum number ‘ni’ to the lower energy state with quantum number nf(nf<ni) , the difference of energy is carried away by a photon of frequency vif such that

hvif=Eni−Enf

Since both nf and ni are integers, this immediately shows that in transitions between different atomic levels, light is radiated in various discrete frequencies. For the hydrogen spectrum, the results of the Bohr’s model suggested the presence of other series spectra for hydrogen atoms corresponding to transitions resulting from nf=1 and ni=2,3,etc.; nf=3&ni=4,5,etc. and so on.

Such series were identified in the course of spectroscopic investigations and are known as the Lyman, Balmer, Paschen, Brackett, and Pfund series. the electronic transitions corresponding to these series shown in the below diagram,

Hence, from the above hydrogen spectrum, the series which lies in the ultraviolet region is the Lyman series.

**Ques. Give an account of the spectral series of hydrogen atoms. (5 Marks)**

**Ans.** Hydrogen atom has a single electron. Its spectrum consists of a series of spectral lines.

**Lyman series:** Lyman Series consists of spectral lines corresponding to the transition of an electron from higher energy orbits n = 1 and n_{2} = 2,3,4… These lines belong to the Ultraviolet region.

**Balmer series:** Balmer series consists of spectral lines emitted during transitions of electrons from higher energy orbits to the second orbit. n_{1} = 2 and n_{2} = 3,4,5… .These lines lie in the visible region.

**Paschen series: **Paschen series consists of spectral lines emitted when an electron jumps higher energy orbits to the third orbit n1 = 3 and n_{2} = 4,5,6 … .These lines lie in the infrared region.

**Brackett series:** Brackett series consists of spectral lines emitted during transitions of electrons from higher energy orbits to fourth orbit. n1 = 4 and n2 = 5,6,7…

**Pfund series:** Pfund series consists of spectral lines emitted during transition of electrons from higher energy orbits to the fifth orbit. n_{1} = 5 and n_{2} = 6,7,8… . These lines lie in the infrared region . The transition from (n_{1}+1) to n1 corresponds to the Ist member or longest wavelength of the series. The transition from (infinity) state to ‘n1’ state corresponds to the last number or series limit or shortest wavelength of the series.

**Read More:-**

Unsaturated Hydrocarbons | Discovery of Electron |

Charge to Mass Ratio of Electron | Limitations of Bohr’s Model |

## FAQs

### What is the wavelength of the line in the spectrum of hydrogen? ›

Solving for the wavelength of this light gives a value of **486.3 nm**, which agrees with the experimental value of 486.1 nm for the blue line in the visible spectrum of the hydrogen atom.

### Why does hydrogen spectrum have 4 lines? ›

Though a hydrogen atom has only one electron, it contains a large number of shells, so when this single electron jumps from one shell to another, a photon is emitted, and the energy difference of the shells causes different wavelengths to be released... hence, mono-electronic hydrogen has many spectral lines.

### What series of lines are in hydrogen spectrum? ›

Hydrogen emission spectrum:

This series of the hydrogen emission spectrum is known as the **Balmer series**. This is the only series of lines in the electromagnetic spectrum that lies in the visible region.

### How many colored lines are in the line spectrum of hydrogen? ›

(b) When the light emitted by a sample of excited hydrogen atoms is split into its component wavelengths by a prism, **four characteristic violet, blue, green, and red** emission lines can be observed, the most intense of which is at 656 nm.

### How do you solve a hydrogen spectrum question? ›

Hydrogen spectrum Solved Numericals - YouTube

### What is the wavelength of first line of Balmer series of hydrogen spectrum? ›

λ=**6569A˚**

### How many spectral lines are emitted from a sample of hydrogen? ›

**Three** spectral lines will be obtained in the line spectrum.

### What is the formula of hydrogen spectrum? ›

Rydberg formula for the spectrum of the hydrogen atom is: **λ1=R(n121−n221)**

### Why do we get so many lines in hydrogen spectrum? ›

A hydrogen atom has only one electron, yet it contains a large number of shells. So, **when this single electron jumps from one shell to another, a photon is emitted, and the energy difference of the shells causes different wavelengths to be released**. Hence, mono-electronic hydrogen has many spectral lines.

### Which of the following about hydrogen spectra is correct Mcq? ›

It lines in infrared region. Since energy of alll the other lines of Paschen series is less than its energy, therefore all the lines of Paschen series will be in infrared region. Hence ,**option ( c)** is also correct.

### Which spectral line has highest wavelength? ›

**Balmer Series**

The longest wavelength is 656.3 nm. The second longest wavelength is 486.1 nm. And the third is 434.1 nm.

### What is the wavelength of Lyman series? ›

Hence the wavelength of the first line in the Lyman series of the hydrogen spectrum is λ=**121.6nm** .

### What are the 3 main colors of the hydrogen spectra? ›

In the lower panel, Hydrogen gas has been excited with electricity in a kind of fluorescent tube, and passed through the prism. The light emanating from the excited hydrogen atoms consists of only four discrete color bands, **red, cyan, blue and violet**.

### What is hydrogen spectrum explain? ›

The hydrogen spectrum is **the electromagnetic radiation emitted by the electron of excited hydrogen while coming to a normal state**. The energy radiated corresponds to its hydrogen spectrum wavelength.

### What is the use of hydrogen spectrum? ›

The spectrum of hydrogen is particularly important in astronomy because most of the universe is made of hydrogen. Emission or absorption processes in hydrogen give rise to series, which are sequences of lines corresponding to atomic transitions, each ending or beginning with the same atomic state in hydrogen.

### How do you find the corrected wavelength? ›

Use the calibration curve from Part 3A to correct for the spectroscope error as follows: Find the spectroscope error (ε) corresponding to your wavelength reading on your graph. Then calculate the corrected wavelength **λ = r + ε** and write this in the table on the line marked “Transition D”.

### How do you find the energy of a spectral line? ›

The change in energy, ΔE, then translates to light of a particular frequency being emitted according to the equation **E=hν**.

### How do I calculate the number of emission lines? ›

Possible spectral lines= **(n2-n1)(n2-n1+1)/2** this is the possible numbers. But in visible region, electron when jumps from n2=5 to n1=1 then according to the formula possible lines=(5-1)(5-1+1)/2=10So the possibilities are 5 to 4, 5 to 3, 5 to 2, 5 to 1, 4 to 3, 4 to 2, 4 to 1, 3 to 2, 3 to 1, 2 to 1.

### What is the wavelength of last line of Balmer series? ›

[ Calculate the wavelength of the 1st and last line in the Balmer series of Hydrogen spectrum. (Ans: **656.5 nm, 364.7 nm**)

### What is the wavelength of second line of Balmer series? ›

The wavelength of the second line in Balmer series of the hydrogen spectrum is **486.4 nm**.

### What is the wavelength of 3rd line of Brackett series in hydrogen spectrum? ›

**λ=21R100**. Was this answer helpful?

### Which series has highest energy in hydrogen spectrum? ›

Energy of electron varies with n21 i.e principal quantum number. For **lyman series** principal quantum number(n) is 1. Hence, Lyman series have highest energy in hydrogen spectrum.

### What is the origin of hydrogen spectrum? ›

The origin of spectral lines in the hydrogen atom (Hydrogen Spectrum) can be explained **on the basis of Bohr's theory**. The hydrogen atom is said to be stable when the electron present in it revolves around the nucleus in the first orbit having the principal quantum number n = 1. This orbit is called the ground state.

### How many possible lines can be observed in the emission spectrum? ›

If an electron moves from n=6 to 5 we get a spectral line. Then from n=5 to 4 we get one and so on giving us a **maximum of 5 spectral lines**.

### What is the frequency of hydrogen? ›

Masers operate at the resonance frequency of the hydrogen atom, which is **1,420,405,752 Hz**.

### What is the energy level of hydrogen? ›

...

Exercise 3.

Energy Level | Energy |
---|---|

5 | -2.176 eV |

### Which hydrogen spectral series is found first? ›

**Lyman series** (n′ = 1)

The series is named after its discoverer, Theodore Lyman, who discovered the spectral lines from 1906–1914. All the wavelengths in the Lyman series are in the ultraviolet band.

### Why does the hydrogen spectrum have the fewest lines? ›

The lines are created when the electrons make transitions from one level to another. **Since Hydrogen has only one electron and since there are only so many allowable transitions**, then the Hydrogen spectrum has the fewest lines.

### Which element produced the largest number of spectral lines? ›

As best understood, the element that has the most lines is **iron** with 235 lines. The greater number of possible lines is due to the varying energies of the atomic orbitals in the energy levels.

### How line spectrum is formed? ›

Spectral lines are produced **by transitions of electrons within atoms or ions**. As the electrons move closer to or farther from the nucleus of an atom (or of an ion), energy in the form of light (or other radiation) is emitted or absorbed.…

### What is the spectrum Mcq? ›

The electromagnetic (EM) spectrum is **the range of all types of EM radiation arranged according to frequency or wavelength**. In order of decreasing wavelength or increasing frequency these are: radio waves radiation, microwave radiation, infrared, visible light, ultraviolet, X-rays, and gamma rays.

### Which of the statement is correct for hydrogen spectrum? ›

**λ1=Z2R(n1−n1)**

### What is a line spectrum Mcq? ›

Explanation: **the plot showing each of harmonic amplitudes in the wave** is called line spectrum. the line rapidly decreases for waves with rapidly convergent series.

### Which series has longest wavelength? ›

**Gamma rays** have the longest wavelength. Gamma rays have the longest wavelength.

### Which series of hydrogen spectrum which has least wavelength? ›

Solution : (i) **Lyman series** has least wavelength.

### What is maximum wavelength? ›

Maximum wave length is obtained when the electrons transition is from n_{1}= 3 to n_{2}= 2. Minimum wave Length is obtained when the electrons transition is from. n_{1}= 2 to n_{2}= infinite. As you know, to calculate the wavelengths, we have equation, **R[1/n _{1}^{2} - 1/n_{2}^{2}]** So for maximum wavelength.

### What is the wavelength of the first line of Paschen series? ›

Wavelength of the first line of Paschen series is − R = **109700 cm − 1**.

### What is the shortest wavelength of Balmer series? ›

The shortest wavelength in the Balmer series is (**R = 1.097 × 107 m-1**)

### Is Balmer series visible? ›

**Balmer series lies in the visible region of the electromagnetic spectrum**.

### What are the 3 types of hydrogen? ›

3 Main Types of Hydrogen - **Blue, Grey and Green** - Brunel.

### What are types of hydrogen? ›

**Green hydrogen, blue hydrogen, brown hydrogen and even yellow hydrogen, turquoise hydrogen and pink hydrogen**. They're essentially colour codes, or nicknames, used within the energy industry to differentiate between the types of hydrogen.

### What colour is hydrogen? ›

Hydrogen itself is has no colour. The colourless gas is an efficient, climate-neutral energy source for heating, as it has a much higher thermal value than, for example, fuel oil or natural gas, and its combustion does not produce any substances that are harmful to the environment or the climate.

### Why does hydrogen spectrum have 4 lines? ›

Though a hydrogen atom has only one electron, it contains a large number of shells, so when this single electron jumps from one shell to another, a photon is emitted, and the energy difference of the shells causes different wavelengths to be released... hence, mono-electronic hydrogen has many spectral lines.

### Who discovered the hydrogen spectrum? ›

In 1953 American physicist **Curtis Humphreys** (1898–1986) discovered the hydrogen spectral line series in which n_{1} = 6 and n_{2} ≥ 7.

### Is hydrogen spectrum continuous? ›

If you use something like a prism or diffraction grating to separate out the light, for hydrogen, **you don't get a continuous spectrum**. You'd see these four lines of color. So, since you see lines, we call this a line spectrum. So this is the line spectrum for hydrogen.

### How many hydrogen spectrums are there? ›

This is called Hydrogen atomic spectrum. The spectral lines are formed due to electronic transitions from one energy level to another. These lines are divided into **five series** according to the range of wavelengths as follows.

### What is the wavelength of hydrogen? ›

The visible spectrum of light from hydrogen displays four wavelengths, **410 nm, 434 nm, 486 nm, and 656 nm**, that correspond to emissions of photons by electrons in excited states transitioning to the quantum level described by the principal quantum number n equals 2.

### What are the 5 series in hydrogen spectrum? ›

**Balmer, Lyman, Paschen, brackett, and Pfund** series are subsequently found in spectral series of the hydrogen spectrum at different wavelengths.

### How do you find the wavelength of a spectral line? ›

Again he gave a formula known as the Rydberg formula to calculate the wavelength of these spectral lines. **1/λ = RZ2(1/n12− 1/n2h)**.

### How do you calculate the wavelength of a line? ›

8.4fCalculating the wavelength of a line in the spectrum of hydrogen

### Why emission spectrum of hydrogen atom is a line spectrum? ›

The emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given by the Rydberg formula. These observed spectral lines are **due to the electron making transitions between two energy levels in an atom**.

### What do you mean by line spectra of hydrogen? ›

The emission spectrum of hydrogen or line spectrum of hydrogen is **produced when hydrogen gas is taken in the discharge tube and the light emitted on passing electric discharge at low pressure is examined with a spectroscope**. It is found to consist of a large number of lines that are grouped into different series.

### What is the formula of hydrogen spectrum? ›

Rydberg formula for the spectrum of the hydrogen atom is: **λ1=R(n121−n221)**

### How do you find the number of spectral lines in hydrogen spectrum? ›

Number of Spectral Lines in Hydrogen Spectrum in Bohr's atomic model ...

### How do you find wavelength from energy? ›

Wavelength is related to energy and frequency by **E = hν = hc/λ**, where E = energy, h = Planck's constant, ν = frequency, c = the speed of light, and λ = wavelength. Wavelength the distance between any given point and the same point in the next wave cycle.

### What's the units for wavelength? ›

Units of Wavelength

The SI unit of wavelength is **meter** because the wavelength is a measure of distance. As a measure of speed and distance, one meter is defined as the distance covered by light travelling in a vacuum in a duration of 1/ (3 x 10 8 ) seconds.

### How do you find the wavelength when given the frequency? ›

Wavelength can be calculated using the following formula: wavelength = wave velocity/frequency. Wavelength usually is expressed in units of meters. The symbol for wavelength is the Greek lambda λ, so λ = v/f.

### What is the wavelength of a spectral line produced when an electron? ›

=**486 nm**.

### What is the use of hydrogen spectrum? ›

The spectrum of hydrogen is particularly important in astronomy because most of the universe is made of hydrogen. Emission or absorption processes in hydrogen give rise to series, which are sequences of lines corresponding to atomic transitions, each ending or beginning with the same atomic state in hydrogen.

### How many spectral lines are emitted from a sample of hydrogen? ›

**Three** spectral lines will be obtained in the line spectrum.

### What is the frequency of hydrogen? ›

Masers operate at the resonance frequency of the hydrogen atom, which is **1,420,405,752 Hz**.

### Is hydrogen spectrum a dark line spectrum? ›

Hydrogen spectrum consists of discrete bright lines in a dark background and it is specifically known as hydrogen emission spectrum. There is one more type of hydrogen spectrum that exists where - Physics. R n 1 λ = R ( 1 2 2 - 1 n 2 ) , where n = 3, 4, 5,....

### What is a line spectra explain their importance class 11? ›

**When atoms are excited they emit light of certain wavelengths which correspond to different colors**. The emitted light can be observed as a series of colored lines with dark spaces in between; this series of colored lines is called a line or atomic spectra. Each element produces a unique set of spectral lines.

### How many lines are in the Lyman series? ›

...

The Lyman series.

n | Wavelength (nm) |
---|---|

11 | 91.9351334 |

∞, the Lyman limit | 91.1753 |