JEE Advanced 2018 Paper 1 · Physics · Atoms, Nuclei and Dual Nature of Radiation · medium

A hydrogen-like ion Li^2+ (Z=3) in its second excited state makes a transition to the first excited state. The emitted photon falls on a metal plate…

One or more options correct

A hydrogen-like ion

\mathrm{Li^{2+}}

(

Z=3

) in its second excited state makes a transition to the first excited state. The emitted photon falls on a metal plate of work function

14.0\ \mathrm{eV}

. Use

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

and

hc=1240\ \mathrm{eV\,nm}

. Which of the following is/are correct?

A. The photon energy is $1.89\ \mathrm{eV}$ .
B. The maximum kinetic energy of the emitted photoelectrons is $3.0\ \mathrm{eV}$ .
C. The stopping potential is $17\ \mathrm{V}$ .
D. The wavelength of the photon is about $730\ \mathrm{nm}$ .

Show answer and solution

Answer: B

The second excited state is

n=3

and the first excited state is

n=2

. The photon energy is

E=13.6\times9\left(\tfrac14-\tfrac19\right)=17.0\ \mathrm{eV}

; the value

1.89\ \mathrm{eV}

is the hydrogen (

Z=1

) Balmer value of the same transition, so (A) is false. The photoelectric equation gives

K_{max}=17.0-14.0=3.0\ \mathrm{eV}

, so (B) is true. The stopping potential is

K_{max}/e=3.0\ \mathrm{V}

, not

17\ \mathrm{V}

, so (C) is false. The wavelength is

\lambda=1240/17.0\approx73\ \mathrm{nm}

, which is in the ultraviolet and not

730\ \mathrm{nm}

, so (D) is false.

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