Question

If $E_1,E_2$ and $E_3$ are the kinetic energies of a proton, $\alpha$ -particle and deuteron respectively, which all have the same wavelength, then

• A. $E_1>E_2>E_3$
• B. $E_1>E_3>E_2$
• C. $E_3>E_2>E_1$
• D. $E_3>E_1>E_2$

Answer 1

Answer: (B)

$E_1>E_3>E_2$

The wavelength $\lambda$ is same for all three particles.
$\lambda =\frac{h}{mu}$
$m$ is mass and $u$ is velocity.
The product $mu$ will also be same.
The particle with higher m value will have lower u value
The kinetic energy $=\frac{1}{2}m{u}^2=\frac{1}{2}\times mu\times u$
The particle with lower u value will have lower kinetic energy.
Thus, the particle with higher $m$ value will have lower kinetic energy.
The increasing order of mass is $m_1<m_3<m_2$.
The decreasing order of kinetic energy is $E_1>E_3>E_2$.
Note:, $m_1$, $m_2$ and $m_3$ are masses of proton, $\alpha$ particle and deuteron respectively.