PROBLEM 109P

The wave nature of matter was first proposed by Louis de Broglie, who suggested that the wavelength (λ) of a particle was related to its mass (m) and its velocity (v) by the equation: λ = h/mv, where h is Planck's constant (6.626 × 10−34J·s). Calculate the de Broglie wavelength of: (a) a 0.0459 kg golf ball traveling at 95 m/s; (b) an electron traveling at 3.88 × 106m/s. Can you explain why the wave nature of matter is significant for the electron but not for the golf ball? (Hint: Express mass in kilograms.)

Solution 109P

Here we have to calculate the de Broglie wavelength for golf ball and electron.

Explain why the wave nature of matter is significant for the electron but not for the golf ball?

Explanation:

Step 1:

(a) Mass of ball = 0.0459 kg velocity = 95 m/s

de Broglie wavelength λ = h/mv

Now, substituting the values, the above equation will be,

λ = 6.626 × 10−34J·s/0.0459 kg 95 m/s

= 1.52 × 10−34 m

Thus the wavelength of golf ball is 1.52 × 10−34 m

Step 2:

(b) Mass of electron =9.1× 10−31kg velocity = 3.88 × 106m/s

de Broglie wavelength λ = h/mv

Now, substituting the values, the above equation will be,

λ = 6.626 × 10−34J·s/9.1× 10−31kg 3.88 × 106m/s

=1.89 × 10−10 m 1.9 × 10−10 m

Thus the wavelength of electron is 1.9 × 10−10 m.