If the wavelength for an electron emitted from H atom is 3.3 10^ … - Vidyadip

MCQ

If the wavelength for an electron emitted from $H$ atom is $3.3 \times 10^{-10}\,m$, then energy absorbed by the electron in its ground state compared to minimum energy required for its escape from the atom, is $.......$times. (Nearest integer).

[Given $: h =6.626 \times 10^{-34}\,Js$,Mass of electron $=9.1 \times 10^{-31}$ ]

A
$1$
B
$3$
✓
$2$
D
$0$

✓

Answer

Correct option: C.

$2$

c
$\lambda=\frac{ h }{\sqrt{2 mK }}$

$K =\frac{ h ^{2}}{2 m \lambda^{2}}$

$K =\frac{ h ^{2}}{2 m \lambda^{2}}=\frac{43.9 \times 10^{-68}}{2 \times 9.1 \times 10^{-31} \times 10.89 \times 10^{-20}}$

$K =2.215 \times 10^{-18}$

$E _{ abs }= E _{\text {req }}+ K$

$\frac{ E _{\text {abs }}}{ E _{\text {req }}}=1+\frac{ K }{ E _{\text {req }}}=1+\frac{2.215 \times 10^{-18}}{13.6 \times 1.602 \times 10^{-19}}=2.0166$

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