JEE Main 2016 · Physics · Atoms, Nuclei and Dual Nature of Radiation · medium

The photon emitted when the electron of a doubly ionised lithium ion Li^2+ jumps from the n=3 to the n=2 level falls on a metal of work function 4…

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The photon emitted when the electron of a doubly ionised lithium ion

\mathrm{Li^{2+}}

jumps from the

n=3

to the

n=2

level falls on a metal of work function

4\ \mathrm{eV}

. Using the hydrogen ground state energy

-13.6\ \mathrm{eV}

, the maximum kinetic energy of the photoelectrons is

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Answer: (B) $13.0\ \mathrm{eV}$

For a hydrogen-like ion

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

. With

Z=3

, the photon energy is

h\nu=13.6\times9\left(\dfrac14-\dfrac19\right)=13.6\times9\times\dfrac{5}{36}=17.0\ \mathrm{eV}

. By the photoelectric equation,

K_{max}=h\nu-\phi=17.0-4=13.0\ \mathrm{eV}

. Quoting the photon energy as the kinetic energy ignores the work function, while adding

\phi

instead of subtracting it gives

21\ \mathrm{eV}

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