Question

A. The mass of an electron is 9.11×10−31 kg. If the de Broglie wavelength for an electron in a hydrogen atom is 3.31×10−10 m, how fast is the electron moving relative to the speed of light? The speed of light is 3.00×108 m/s. Calculate your answer as a percentage.The solution was .732% B. The mass of a golf ball is 45.9 g . If it leaves the tee with a speed of 70.0 m/s , what is its corresponding wavelength? Compare your answer with the wavelength of the electron given in Part A. Please solve part B

Answer 1

PART A:

Since

λ = h / p

Where, p = momentum

h = Planck’s Constant

And, p = mass x velocity

So, v= h / (m λ)

v = 6.626x10^-34 / (9.11x10^-31*3.31x10^-10) = 2.197x10^6 m/s

v / c % = ( 2.197x10^6 / 3x10^8 ) x 100= 0.732%

PART B:

λ = h / p = h / mv

Where, m = mass

v = velocity

h = Planck’s Constant

λ = 6.626 x 10-34kg·m²/s / (0.0459kg*70.0m/s) = 2.06 x 10^-34 m

As, we can see from the results, the wavelength of ball is very less compared to wavelength of electron.