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Class 12
Physics
Atoms
a hydrogen atom initially in the ground level abso...

Question:
A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of the photon.

Answer:

For ground level, n ₁= 1

Let E₁ be the energy of this level. It is known that E₁ is related with n₁ as:

E₁ = -13.6/n₁² eV

= -13.6/1² = -13.6 eV

The atom is excited to a higher level, n² = 4.

Let E² be the energy of this level.

∴ E₂ = -13.6/n₂² eV

= -13.6/4² = -13.6/16 eV

The amount of energy absorbed by the photon is given as:

E = E₂ - E₁

= (-13.6 /16) - (-13.6/1)

= 13.6 X 15/16 eV

= (13.6 X 15/16) X 1.6 X 10^-19 = 2.04 X 10^-18 J

For a photon of wavelengthλ, the expression of energy is written as:

E = hc/λ

Where,

h = Planck’s constant = 6.6 × 10⁻³⁴ Js

c = Speed of light = 3 × 10⁸ m/s

∴ λ = hc/E

= (6.6x10^-34x3x10⁸)/(2.04x10^-18)

= 9.7x10^-8 m = 97 nm

And, frequency of a photon is given by the relation,

v = c/λ

= (3x10⁸)/(9.7x10^-8) ≈ 3.1 x 10¹⁵ Hz

Hence, the wavelength of the photon is 97 nm while the frequency is 3.1 × 10¹⁵ Hz.

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Question:
A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of the photon.

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Question: A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of the photon.

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Question:
A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of the photon.