Question

The increasing order of wavelength for $H{e}^{+}$ ion, neutron(n) and electron (e) particles, moving with the same velocity is:

• A. ${\lambda }_{H{e}^{+}}<{\lambda }_e<{\lambda }_n$
• B. ${\lambda }_{H{e}^{+}}={\lambda }_n={\lambda }_e$
• C. ${\lambda }_{H{e}^{+}}<{\lambda }_n<{\lambda }_e$
• D. ${\lambda }_e<{\lambda }_n<{\lambda }_{H{e}^{+}}$

Answer 1

The correct option is C ${\lambda }_{H{e}^{+}}<{\lambda }_n<{\lambda }_e$

$\because \lambda =\frac{h}{m.v}$
(As per de-Broglie relation)

$\therefore \lambda \propto \frac{1}{m}$ (h and v are constant)
Also, $\because m_{H{e}^{+}}>m_n>m_e$

$\therefore {\lambda }_{H{e}^{+}}<{\lambda }_n<{\lambda }_e$.