Question

If E is the energy of orbit of hydrogen atom the energy of n^th orbit of He atom will be

• A. E
• B. 2E
• C. 3E
• D. 4E

Answer 1

Answer: (D)

4E

Answer 2

Since Bohr’s formula for energy in nth orbit is

$E_{n} = - \frac{me^{4}Z^{2}}{8\varepsilon_{0}^{2}n^{2}h^{2}}$

$\Rightarrow E_{n} \propto Z^{2}$

Now for hydrogen

$(_{1}H^{2}),Z_{H} = 1$ and $E_{H} = E$ and for helium

$(_{2}He^{4})Z_{He} = 2$

$\therefore\frac{E_{H}}{E_{He}} = \frac{(Z_{H})^{2}}{(Z_{He})} \Rightarrow E_{He} = \left( \frac{Z_{He}}{Z_{H}} \right)^{2}E_{H}$

$= (2)^{2}E = 4E$