In order to coincide the parabolas formed by singly ionised ions … - Vidyadip

MCQ

In order to coincide the parabolas formed by singly ionised ions in one spectrograph and doubly ionized ions in the other Thomson's mass spectrograph, the electric fields and magnetic fields are kept in the ratios $1: 2$ and $3: 2$ respectively. Then the ratio of masses of the ions is

A
$3: 4$
B
$1: 3$
✓
$9: 4$
D
None of these

✓

Answer

Correct option: C.

$9: 4$

Using $Z^2=k\left(\frac{q}{m}\right) y$; where $k=\frac{B^2 L D}{E}$.
For parabolas to coincide in the two photographs, the $\frac{k q}{m}$ should be same for the two cases.
Thus,$\frac{B_1^2 L D e}{E_1 m_1}=\frac{B_2^2 L D(2 e)}{E_2 m_2}$
$\Rightarrow \frac{m_1}{m_2}=\left(\frac{B_1}{B_2}\right)^2 \times\left(\frac{E_2}{E_1}\right) \times \frac{1}{2}=\frac{9}{4} \times \frac{2}{1} \times \frac{1}{2}=\frac{9}{4}$

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