Question

The de Broglie wavelength of a 100-m sprinter of mass 66 kg running at a speed of
10 m/s is about

Answer 1

To calculate the de Broglie wavelength for a particle, or for a tennis ball for that matter, just use the equation. p=hλ , where. p - the momentum of the atom; h - Planck's constant - 6.626⋅10−34m2kg s− 1

Answer 2

Given:

• Mass of runner = 66 kg
• Velocity = 10 m/s

To find:

• De-Broglie wavelength associated with the runner ?

Calculation:

The general equation of De-Broglie wavelength for any particle is given as :

$\boxed{ \lambda = \dfrac{h}{m \times v} }$

• 'h' is Planck's Constant, 'm' is mass and 'v' is velocity.

• Putting necessary values in SI UNITS:

$\implies\lambda = \dfrac{6.626 \times {10}^{ - 34} }{66 \times 10}$

$\implies\lambda = \dfrac{6.626 \times {10}^{ - 34} }{660}$

$\implies\lambda = \dfrac{6.626 \times {10}^{ - 35} }{66}$

$\implies\lambda \approx 0.1003 \times {10}^{ - 35} \: m$

So, the De-Broglie wavelength associated with the runner is approximately equal to 0.1003 × 10^(-35) metres.