Question

Practice Problem 7.6 Calculating the de Broglie Wavelength of an Electron Find the deBroglie wavelength of 39.7 g racquetball travelling at a speed of 55 mi/hr. (6.7 x 1034 m) Proble Qu

Answer 1

Step 1: Explanation

To calculate the deBroglie wavelength for a particle, just use the equation

p = h /λ, where

p = the momentum of the particle
h = Planck's constant = (6.626 ×10^-34 m²kg s^-1 )
λ =  wavelength

Momentum can be expressed as

p = mv, where

m = the mass of the particle;
v = the speed of the particle.

on substituting the value p = mv

=> p = h /λ

=> mv = h /λ

=> λ = h / mv

Step 2: Calculation

Given,

mass(m) = 39.7 g = 39.7 × 10^-3 kg [ note: 1 g = 10^-3 kg hence, 39.7 g × (10^-3 kg / 1 g ) = 39.7 × 10^-3 kg ]

velocity (v) = 55 mi/hr = 24.5872 m/s

[ note: 1 mi /hr = 0.44704 m/s hence, 55 mi/hr × ( 0.44704 m/s / 1 mi/hr ) = 24.5872 m/s

hence on substituting the value in above equation we get

λ = h / mv

λ = 6.626 ×10^-34 m²kg s^-1 / ( 39.7 × 10^-3 kg × 24.5872 m/s ) = 6.7 × 10^-34 m