Answer to Question #193769 in Mechanics | Relativity for jay

Question

What is the de Broglie wavelength for a particle moving with

speed 2.0 × 106 m/s if the particle is (a) an electron, (b) a proton,

and (c) a 0.20-kg ball?

Answer 1

Gives

Particle velocity (v)=$2\times10^6m/sec$

(a)

Particle electron

$\lambda_e=\frac{h}{m_ev} \rightarrow(1)$

For electron

$h=6.625\times10^{-34}Jsec$

$m_e=9.1\times10^{-31}kg$

Put value equation (1)

$\lambda=\frac{6.625\times10^{-34}}{9.1\times10^{-31}\times2\times10^6}$

$\lambda= 3.65\times10^{-10}meter=3.65\text{\AA}$

(b)

Particle proton

$\lambda_{p}=\frac{h}{m_pv} \rightarrow(2)$

$\lambda_{p}=\frac{6.625\times10^{-34}}{1.67\times10^{-27}\times2\times10^6}$

$\lambda_{p}=1.983\times10^{-13}meter$

(c)$\lambda_{ball}=\frac{h}{m_{ball}v} \rightarrow(3)$

$m_{ball}=0.20kg$

$\lambda_{ball}=\frac{6.625\times10^{-34}}{0.20\times2\times10^6}$

$\lambda_{ball}=1.65\times10^{-39}meter$