A sample consisting of Hydrogen atoms in the ground state is excited by monochromatic radiation of energy 12.75eV . If we were to observe the emission spectrum of this sample, then the number of spectral lines observed, will be

Question

A sample consisting of Hydrogen atoms in the ground state is excited by monochromatic radiation of energy 12.75eV . If we were to observe the emission spectrum of this sample, then the number of spectral lines observed, will be (A) 3 (B) 6 (C) 10 (D) 15

Tardigrade Admin · Accepted Answer

The energy of an electron of a hydrogen atom in the ground state is

E_{0} = - 13.6 e V

The energy of incoming photon =

12.75 e V

The energy of an electron in the excited state is

- \frac{13.6}{n ^{2}} = - 13.6 + 12.75 = - 0.85 e V

\Rightarrow n^{2} = \frac{13.6}{0.85} = 16

\Rightarrow n = 4

No. of spectral lines =

\frac{n ( n - 1 )}{2}

=

6

Q. A sample consisting of Hydrogen atoms in the ground state is excited by monochromatic radiation of energy $12.75 e V$ . If we were to observe the emission spectrum of this sample, then the number of spectral lines observed, will be

$3$

$6$

$10$

$15$

Q. A sample consisting of Hydrogen atoms in the ground state is excited by monochromatic radiation of energy 12.75eV . If we were to observe the emission spectrum of this sample, then the number of spectral lines observed, will be

3

6

10

15

The energy of an electron of a hydrogen atom in the ground state is E0​=−13.6eV The energy of incoming photon = 12.75eV The energy of an electron in the excited state is −n213.6​=−13.6+12.75=−0.85eV ⇒n2=0.8513.6​=16 ⇒n=4 No. of spectral lines = 2n(n−1)​ = 6

Q. A sample consisting of Hydrogen atoms in the ground state is excited by monochromatic radiation of energy $12.75 e V$ . If we were to observe the emission spectrum of this sample, then the number of spectral lines observed, will be

$3$

$6$

$10$

$15$