Question

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?

Answer 1

These are two questions and two answers

Question 1.

Answer:

• 7.33 × 10 ⁻³ c

Step-by-step 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:

• λ = h / (m.s)

• h is Planck's constant: h= 6.626×10⁻³⁴J.s

3) Solution:

Solve for s:

• s = h / (m.λ)

Substitute:

• s = 6.626×10⁻³⁴J.s / ( 9.11 × 10⁻³¹ kg × 3.31 × 10⁻¹⁰ m) = 2.20 × 10 ⁶ m/s

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

• s = 2.20 × 10 ⁶ m/s / 3.00 10⁸ m/s = 7.33 × 10 ⁻³

Answer: s = 7.33 × 10 ⁻³ c

Question 2.

Answer:

• 2.06 × 10 ⁻³⁴ m.

Step-by-step 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:

• λ = h / (m.s)

• h is Planck's constant: h= 6.626×10⁻³⁴J.s

3) Solution:

• λ = h / (m.s)

Substitute:

• λ = 6.626×10⁻³⁴J.s / ( 0.0459 kg × 70.0 m/s) = 2.06 × 10 ⁻³⁴ m

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

Answer: 2.06 × 10 ⁻³⁴ m.