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On the basis of Bohr’s theory, derive an expression for the radius of the orbit of an electron of…
(a)
On the basis of Bohr’s theory, derive an expression for the radius of the $n^{\text{th}}$ orbit of an electron of hydrogen atom.
Given: Bohr's postulates: $mvr = \frac{nh}{2\pi}$ and $\frac{mv^2}{r} = \frac{1}{4\pi\varepsilon_0}\frac{e^2}{r^2}$
To show: $r_n = \frac{\varepsilon_0 n^2 h^2}{\pi m e^2}$
(b)
Calculate the energy released in the following nuclear fusion reaction:
${}^2_1\text{H} + {}^2_1\text{H} \to {}^4_2\text{He} + \text{energy}$
Mass of ${}^2_1\text{H} = 2.014102\text{ u}$
Mass of ${}^4_2\text{He} = 4.002604\text{ u}$
Answer
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From ISC 2024 Physics Paper 1, question 19(i).