Question

An element undergoes a reaction as shown:
$X+2e^{-}\to X^{2-}$, energy released $=30.87eV/atom$. If the energy released , is used to dissociate $4gms$ of $H_2$ molecules, equally into $H^{+}$ and $H^{\ast }$, where $H^{\ast }$ is excited state of $H$ atoms where the electron travels in orbit whose circumference equal to four times its de Broglie's wavelength. Determine the least moles of $X$ that would be required:
Given $I.EofH=13.6eV/atom$, bond energy of $H_2=4.526eV/molecule$

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2

$2\pi r=4\lambda ;n=4$
Total energy required $+$total energy released $=0$
$2\times 4.526eV\times N_A+2\times 13.6\times N_A+2\times 13.6\times (1-\frac{1}{16})\times N_A-30.87\times x\times N_A=0$
$x=2,\therefore$moles of $X$ required $=2$