JEE Advanced 2021 Paper 1 · Physics · Atoms, Nuclei and Dual Nature of Radiation · medium

A sample of atomic hydrogen has all its atoms in the n=5 state and de-excites by emitting every possible spectral line. The light falls on a metal of…

Numerical answer

A sample of atomic hydrogen has all its atoms in the

n=5

state and de-excites by emitting every possible spectral line. The light falls on a metal of work function

2.50\ \mathrm{eV}

. Use

E_n=-13.6/n^{2}\ \mathrm{eV}

and neglect recoil. How many distinct spectral lines liberate photoelectrons whose stopping potential is less than

10.0\ \mathrm{V}

Show answer and solution

Answer: 4

Atoms excited to

n=5

(and their cascades) give all

\binom52=10

lines. A line produces photoelectrons only if

h\nu>2.50

eV, and the stopping potential is

(h\nu-2.50)/e<10.0

V, i.e.

2.50<h\nu<12.50

eV. The photon energies (eV) are:

5\to4

: 0.31;

4\to3

: 0.66;

5\to3

: 0.97;

3\to2

: 1.89 (all below the work function);

4\to2

: 2.55;

5\to2

: 2.86;

2\to1

: 10.20;

3\to1

: 12.09 (these four lie within the window);

4\to1

: 12.75 and

5\to1

: 13.06 (stopping potentials 10.25 V and 10.56 V, too large).

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