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Cut-off Wavelength

In a particle...

Question

In a particle accelerator, a beam of proton is emitted at $1.5 \times 10^{7} m s^{- 1}$ . The beam of some protons strike head on with gas atoms and rebound at $1.2 \times 10^{7} m s^{- 1}$ . If the initial velocity of gas atom is negligible, find the mass of gas atom in terms of mass of proton : (Assume mass of proton is $m$ )

A

\frac{1}{3}

m

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B

\frac{1}{6}

m

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C

1 m

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D

\frac{1}{9}

m

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E

\infty

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Solution

The correct option is E $\frac{1}{9}$ m
Let's assume mass of gas atoms is $m_{2}$ . Before collision velocity of proton is $u_{1}$ and velocity of gas atom is $u_{2}$ . After the collision the velocity of proton is $v_{1}$ then

$v_{1} = \frac{(m_{1} - m_{2})}{m_{1} + m_{2}} u_{1} + \frac{2 m_{2} u_{2}}{m_{1} + m_{2}}$

Putting the values of $m_{1}, u_{1}, v_{1}$ and $u_{2} = 0$

$\Rightarrow 1.2 \times 10^{7} = \frac{m - m_{2}}{m + m_{2}} (1.5 \times 10^{7})$

$\Rightarrow m_{2} = \frac{1}{9} m$

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