Question

Find the de Broglie wavelength of Earth. Mass of Earth is 6 × 10²⁴ kg. Mean orbital radius of Earth around Sun is 150 × 10⁶ km

• A. 3.7 m
• B. 3.7 × 10^–63 m
• C. 3.7 × 10⁶³ m
• D. 3.7 × 10^–63 cm

Answer 1

Answer: (B)

3.7 × 10^–63 m

Answer 2

The Earth revolves around the Sun once a year and its orbit has a mean radius 150 × 10⁶ km. Hence its average orbital speed is

v =$\frac{2\pi \times 150 \times 10^{9}}{365 \times 24 \times 3600}$= 3 × 10⁴ m s^–1

As the Earth has mass 6 × 10²⁴ kg, its average momentum is

p = mv = 1.8 × 10²⁹ kg m s^–1

and so its de Broglie wavelength is

l =$\frac{h}{p}$=$\frac{6.63 \times 10^{- 34}}{1.8 \times 10^{29}}$= 3.7 × 10^–63 m,

If the Sun can be considered stationary