Monochromatic radiation of wavelength λ is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. Find the value of λ .

Question

Monochromatic radiation of wavelength λ is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. Find the value of λ . (A) 102nm (B) 100nm (C) 97.5nm (D) 94.5nm

Tardigrade Admin · Accepted Answer

As the hydrogen atoms emit radiation of six different wavelengths, some of them must have been excited to

n = 4

, The energy in

n = 4

state is

E_{4} = \frac{E _{1}}{4 ^{2}} = - \frac{13 \cdot 6 e V}{16} = - 0 \cdot 85 eV.

The energy needed to take a hydrogen atom from its ground state to

n = 4

is

13 .6 eV - 0 .85 eV = 12 .75 eV

.
The photons of the incident radiation should have

12.75 eV

of energy. So

\frac{hc}{λ} = 12 \cdot 75 eV

or ,

λ = \frac{hc}{12 \cdot 75 eV}

= \frac{1242 eV nm}{12 \cdot 75 eV}

= 97 .5 nm

.

Q. Monochromatic radiation of wavelength $λ$ is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. Find the value of $λ$ .

$102 nm$

$100 nm$

$97.5 nm$

$94.5 nm$

Q. Monochromatic radiation of wavelength λ is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. Find the value of λ .

102nm

100nm

97.5nm

94.5nm

Q. Monochromatic radiation of wavelength $λ$ is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. Find the value of $λ$ .

$102 nm$

$100 nm$

$97.5 nm$

$94.5 nm$