The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100 V. What should nearly be the ratio of their wavelengths ? ( m P =1.00727 u , m e =0.00055 u )

Question

The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100 V. What should nearly be the ratio of their wavelengths ? ( m P =1.00727 u , m e =0.00055 u ) (A) 1860: 1 (B) (1860)2: 1 (C) 41.4: 1 (D) 43: 1

Tardigrade Admin · Accepted Answer

λ=( h / mv )=( h /√2 mK )=( h /√2 mqV ) (λ1/λ2)=√( m 2/ m 1) (λ e /λ p )=√( m P / m e )=√1831.4=42.79

Q. The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of $100 V$ . What should nearly be the ratio of their wavelengths ? $(m_{P} = 1.00727 u, m_{e} = 0.00055 u)$

$1860 : 1$

$(1860)^{2} : 1$

$41.4 : 1$

$43 : 1$

$λ = \frac{h}{m v} = \frac{h}{2 m K} = \frac{h}{2 m q V}$
$\frac{λ _{1}}{λ _{2}} = \frac{m _{2}}{m _{1}}$
$\frac{λ _{e}}{λ _{p}} = \frac{m _{P}}{m _{e}} = 1831.4 = 42.79$

Q. The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100V. What should nearly be the ratio of their wavelengths ? (mP​=1.00727u,me​=0.00055u)

1860:1

(1860)2:1

41.4:1

43:1