Question

A green ball weighs 80 g and comes travelling towards you at 900 m/s. A photon of light emitted from green ball has a wavelength of $6\times {10}^{-7}$ m. Assuming that the error in the position of ball is the same as the wavelength of its photon, calculate error in the momentum (kgm/s) of the green ball.

• A. $1.054\times {10}^{-30}$
• B. $1.054\times {10}^{-23}$
• C. $2.786\times {10}^{-23}$
• D. $8.75\times {10}^{-29}$

Answer 1

The correct option is D $8.75\times {10}^{-29}$

m = 80 g, v = 900 m/sec ,
$\Delta x$ = $6\times {10}^{-7}$ m,
According to heisenberg's uncertainty principle,
$\Delta x.\Delta p\ge \frac{h}{4\pi }$
$\Delta p\ge \frac{h}{4\pi \times \Delta x}$
$\ge \frac{6.6\times {10}^{-34}}{4\times 3.14\times 6\times {10}^{-7}}$
$\ge 8.75\times {10}^{-29}$ kg m/s