Part 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. part 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?

These are two questions and two answers

Question 1.

Explanation:

1) Data:

a) m = 9.11 × 10⁻³¹ kg

b) λ =  3.31 × 10⁻¹⁰ m

c) c = 3.00 10⁸ m/s

d) s = ?

2) Formula:

The wavelength (λ), the speed (s), and the mass (m) of the particles are reltated by the Einstein-Planck's equation:

3) Solution:

Solve for s:

Substitute:

To express the speed relative to the speed of light, divide by c =  3.00 10⁸ m/s

s = 7.33 × 10 ⁻³ c

Question 2.

Explanation:

1) Data:

a) m = 45.9 g (0.0459 kg)

b) s = 70.0 m/s

b) λ =  ?

2) Formula:

Macroscopic matter follows the same Einstein-Planck's equation, but the wavelength is so small that cannot be detected:

3) Solution:

Substitute:

As you see, that is tiny number and explains why the wave nature of the golf ball is undetectable.

2.06 × 10 ⁻³⁴ m.  

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