Question 97: Dual Nature of Matter and Radiation

Question

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $\lambda$. An alpha particle having certain kinetic energy has the same de-Brogle wavelength $\lambda$. The ratio of kinetic energy of proton and that of alpha particle is:

Accepted Answer

For same $\lambda_{1}$ momentum should be same,
$(P)_{P}=(P)_{\alpha}$
$\Rightarrow \sqrt{2 k_{P} m_{P}}=\sqrt{2 k_{\alpha} m_{\alpha}}$
$\Rightarrow k_{P} m_{P}=k_{\alpha} m_{\alpha}$
$\Rightarrow \frac{k_{P}}{k_{\alpha}}=\left(\frac{m_{\alpha}}{m_{P}}\right)=\frac{4}{1}=4: 1$

Answer

1 : 4

Answer

2 : 1

Answer

4 : 1

Answer

1 : 2

Dual Nature of Matter and Radiation

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of \lambda. An alpha particle having certain kinetic energy has the same de-Brogle wavelength \lambda. The ratio of kinetic energy of proton and that of alpha particle is:

Choose the correct answer: