A hydrogen atom in its ground state is irradiated by light of wavelength . Taking and the ground state energy of hydrogen atom as , the number of lines present in the emission spectrum is [2016]

Question

A hydrogen atom in its ground state is irradiated by light of wavelength $970 Å$ . Taking $\frac{h c}{e} = 1.237 \times 10^{- 6} eV m$ and the ground state energy of hydrogen atom as $- 13.6 eV$ , the number of lines present in the emission spectrum is [2016]

Smart Achievers · Accepted Answer

(6)

Energy of incident light,

$E = \frac{h c}{λ} = \frac{1.237 \times 10^{- 6}}{970 \times 10^{- 10}} eV = 12.75 eV$

$∴$ The energy of electron after absorbing this photon $= - 13.6 + 12.75 = - 0.85 eV$

Let the electron jump to the $n^{th}$ state after excitation.

$∴$ $\frac{- 13.6}{n^{2}} = - 0.85$ $∴$ $n = 4$

$∴$ Total number of spectral lines $= \frac{n (n - 1)}{2} = \frac{4 (4 - 1)}{2} = 6$

Solution

Q.
A hydrogen atom in its ground state is irradiated by light of wavelength $970 Å$ . Taking $\frac{h c}{e} = 1.237 \times 10^{- 6} eV m$ and the ground state energy of hydrogen atom as $- 13.6 eV$ , the number of lines present in the emission spectrum is [2016]

Want Us to Email you About Special Offers & Updates?

Solution

Q. A hydrogen atom in its ground state is irradiated by light of wavelength 970 Å. Taking hce=1.237×10-6 eV m and the ground state energy of hydrogen atom as -13.6 eV, the number of lines present in the emission spectrum is [2016]

Ans. (6) Energy of incident light, E=hcλ=1.237×10-6970×10-10 eV=12.75 eV ∴ The energy of electron after absorbing this photon =-13.6+12.75=-0.85 eV Let the electron jump to the nth state after excitation. ∴ -13.6n2=-0.85 ∴ n=4 ∴ Total number of spectral lines =n(n-1)2=4(4-1)2=6

Want Us to Email you About Special Offers & Updates?

Q.
A hydrogen atom in its ground state is irradiated by light of wavelength $970 Å$ . Taking $\frac{h c}{e} = 1.237 \times 10^{- 6} eV m$ and the ground state energy of hydrogen atom as $- 13.6 eV$ , the number of lines present in the emission spectrum is [2016]