Question

An electron of mass ${\mathrm{m}}_{\mathrm{e}}$ and a proton of mass ${\mathrm{m}}_{\mathrm{p}}=$$1836m_e$ are moving at the same speed. The ratio of their de Broglie wavelength ${\mathrm{\lambda }}_{\mathrm{electron}}/{\mathrm{\lambda }}_{\mathrm{proton}}$ will be:

• A. $918$
• B. $1836$
• C. $\frac{1}{1836}$
• D. $1$

Answer 1

The correct option is B

$1836$

The Explanation for the correct option:

we know,

Step 1: De Broglie’s wavelength $=\frac{h}{mv}$

Step 2: for proton,${\mathrm{\lambda }}_{\mathrm{p}}=\frac{\mathrm{h}}{{\mathrm{m}}_{\mathrm{p}}\mathrm{v}}$

for electron, ${\mathrm{\lambda }}_{\mathrm{e}}=\frac{\mathrm{h}}{{\mathrm{m}}_{\mathrm{e}}\mathrm{v}}$

here, ${\lambda }_p=$wavelength of the proton and ${\lambda }_e=$=wavelength of an electron

Step 3:
now,$\frac{{\lambda }_p}{{\lambda }_e}=\frac{h\times m_e\times v}{h\times m_p\times v}$

$=\frac{m_e}{m_p}$

$=\frac{m_e}{1836m_e}$

hence,

$\frac{{\lambda }_e}{{\lambda }_p}=1836$

so, option (B) is correct.