Q86 / 160 · JIPMER 2011 · Physics

The specific charge of a proton is $9.6 \times 10^7 \mathrm{C} / \mathrm{kg}$. The specific charge of an alpha particle will be

  • A
    $9.6 \times 10^7 \mathrm{C} / \mathrm{kg}$
  • B
    $19.2 \times 10^7 \mathrm{C} / \mathrm{kg}$
  • Correct answer
    C
    $4.8 \times 10^7 \mathrm{C} / \mathrm{kg}$
  • D
    $2.4 \times 10^7 \mathrm{C} / \mathrm{kg}$

Solution

Specific charge on proton $=\left(\frac{e}{m}\right)_p$ $=9.6 \times 10^7 \mathrm{C} / \mathrm{kg}$ Specific charge on $\alpha$-particle, $\left(\frac{q}{m}\right)_\alpha=\frac{2 e}{4 m}=\frac{1}{2}\left(\frac{e}{m}\right)_p=\frac{1}{2} \times 9.6 \times 10^7$ $=4.8 \times 10^7 \mathrm{C} / \mathrm{kg}$

Hence, the correct answer is option: 'C'.

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