Question

What is the wavelength of the matter wave associated with a proton moving at 381 m/s?

wavelength of proton matter wave: 1.04×10^9 m

What is the wavelength of the matter wave associated with a 151 kg astronaut (including her spacesuit) moving at the same speed?

wavelength of astronaut matter wave: 1.15×10^-38 m

What is the wavelength of the matter wave associated with Earth moving along its orbit around the Sun?

wavelength of Earth matter wave: ??? m

I got the first two answers by my last answer I put 1.34 x 10^-59 and it was wrong.

Answer 1

m = mass of proton = 1.67 x 10^-27 kg

v = speed of proton = 381 m/s

wavelength is given as

= h/(mv)

= 6.63 x 10^-34 /((1.67 x 10^-27) (381))

= 1.04 x 10^-9 m

For astronaut :

m = mass of astronaut = 151 kg

v = speed of astronaut = 381 m/s

wavelength is given as

= h/(mv)

= 6.63 x 10^-34 /((151) (381))

= 1.15 x 10^-38 m

For earth :

T = Time period = 365 days = 365 x 24 x 3600 sec

angular speed is given as

w = 2/T = 2(3.14)/(365 x 24 x 3600) = 2 x 10^-7 rad/s

r = radius of the orbit = 1.5 x 10¹¹ m

speed is given as

v = r w = (1.5 x 10¹¹) (2 x 10^-7) = 3 x 10⁴ m/s

m = mass of earth = 5.98 x 10²⁴ kg

wavelength is given as

= h/(mv)

= 6.63 x 10^-34 /((5.98 x 10²⁴) (3 x 10⁴))

= 3.7 x 10^-63 m