The energy of hydrogen atom in n text th orbit is En then the energy in n text th orbit of singly ionised helium atom will be

Question

The energy of hydrogen atom in n text th orbit is En then the energy in n text th orbit of singly ionised helium atom will be (A)  4En  (B)  En/4  (C)  2En  (D)  En/2

Tardigrade Admin · Accepted Answer

The energy of the electron in the nth orbit is E = E propto Z2 (1/n2) Given, ZH=1,ZHe=2 ∴ (EH/EHe)= (ZH2/Z2He)= (1/4) ⇒ EHe=4 EH Given, EH=En ∴ EHe=4En

Q. The energy of hydrogen atom in $n^{th}$ orbit is $E_{n}$ then the energy in $n^{th}$ orbit of singly ionised helium atom will be

$4 E_{n}$

$E_{n} /4$

$2 E_{n}$

$E_{n} /2$

The energy of the electron in the $n^{t h}$ orbit is
$E = E \propto Z^{2} \frac{1}{n ^{2}}$
Given, $Z_{H} = 1, Z_{He} = 2$
$∴ \frac{E _{H}}{E _{He}} = \frac{Z _{H}^{2}}{Z _{He}^{2}} = \frac{1}{4}$
$\Rightarrow E_{He} = 4 E_{H}$
Given, $E_{H} = E_{n}$
$∴ E_{He} = 4 E_{n}$

Q. The energy of hydrogen atom in nth orbit is En​ then the energy in nth orbit of singly ionised helium atom will be

4En​

En​/4

2En​

En​/2