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Physics · 2022 · 3 marks
CBSE 2022 · Region 3 · Set 3 · Q11
(a) The energy of hydrogen atom in an orbit is -1.51 eV. What are kinetic and potential energies of the electron in this orbit? (b) The electron in a…
(a)
The energy of hydrogen atom in an orbit is -$\displaystyle 1.51$ eV. What are kinetic and potential energies of the electron in this orbit ?
(b)
The electron in a hydrogen atom is typically found at a distance of about $\displaystyle 5.3 \times 10^{-11} \mathrm{~m}$ from the nucleus which has a diameter of about $\displaystyle 1.0 \times 10^{-15} \mathrm{~m}$. Assuming the hydrogen atom to be a sphere of radius $\displaystyle 5.3 \times 10^{-11} \mathrm{~m}$, what fraction of its volume is occupied by the nucleus?
Marking-scheme solution
(a)
Finding the Kinetic and potential energy of electron $\displaystyle 1$+$\displaystyle 1$
$\displaystyle E=-1.51 \mathrm{eV}$
$\displaystyle K=-E$
$\displaystyle =1.51 \mathrm{eV}$
$\displaystyle U=2 E$
$\displaystyle =-3.02 \mathrm{eV}$
Fraction of volume occupied by the nucleus
$\displaystyle =\frac{\dfrac{4}{3} \pi r^{3} \text { nucleus }}{\dfrac{4}{3} \pi r^{3} \text { atom }}$
$\displaystyle =\left(\frac{r_{\text {nucleus }}}{r_{\text {atom }}}\right)^{3}$
$\displaystyle =\left(\frac{0.5 \times 10^{-15}}{5.3 \times 10^{-11}}\right)^{3}$
$\displaystyle =8.3 \times 10^{-16}$
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CBSE Class 12 Physics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.