Question

How fast must a 54g tennis ball travel in order to have a de Broglie wavelength that is equal to that of a photon of green light 5400Å?

Answer 1

Given conditions ⇒
Mass of the ball = 54 g.
 = 0.054 kg. 
De-Broglie Wavelength = 5400 Angstrom.
 = 5400 × 10⁻¹⁰ m.

Now, Using the Formula,

 λ = h/mv
where,
 h is the plank constant = 6.62 × 10⁻³⁴ J-s.
and v is the velocity of the tennis balls. 

∴ 5400 × 10⁻¹⁰ = (6.62 × 10⁻³⁴)/(0.054 × v)
⇒ 0.054v = (6.62 × 10⁻³⁴)/(5400 × 10⁻¹⁰)
⇒ 0.054v = 0.0012 × 10⁻²⁴
⇒ v = 0.0012 × 10⁻²⁴/0.054
⇒ v = 0.023 × 10⁻²⁴ m/s. 


Hence, the velocity of the tennis balls is 0.023 × 10⁻²⁴ m/s. 


Hope it helps.