Question

An X-rays has a wavelength of 0.01 8. Its momentum is
(a) 3.313 x 10-22 kg-m/s (b) 6.626 x 10-21 kg-m/s
(c) 3.456 x 10-25 kg-m/s (d) 2.126 x 10-22 kg-m/s​

Answer 1

Answer:

$\boxed{\mathfrak{Momentum \ (p) = \ 6.626 \times {10}^{ - 22} \: kg⋅m/s}}$

Given:

Wavelength of X-ray (λ) = 0.01 Å = $\sf 0.01 \times 10^{-10}$ m

Planck's constant (h) = $\sf 6.626 \times 10^{-34}$ m²kg/s

To Find:

Momentum of X-ray (p)

Explanation:

Formula:

$\boxed{ \bold{ \lambda = \frac{h}{p} }}$

$\sf \implies p = \frac{h}{ \lambda}$

Substituting value of λ & h in the equation:

$\sf \implies p = \frac{6.626 \times {10}^{ - 34} }{0.01 \times {10}^{ - 10} } \\ \\ \sf \implies p = \frac{6.626 \times {10}^{ - 34} }{10^{-2} \times {10}^{ - 10} } \\ \\ \sf \implies p = \frac{6.626 \times {10}^{ - 34} }{ {10}^{ -2 + (- 10)} } \\ \\ \sf \implies p = \frac{6.626 \times {10}^{ - 34} }{ {10}^{ -2 - 10} } \\ \\ \sf \implies p = \frac{6.626 \times {10}^{ - 34} }{ {10}^{ - 12} } \\ \\ \sf \implies p = 6.626 \times {10}^{ - 34 - ( - 12)} \\ \\ \sf \implies p = 6.626 \times {10}^{ - 34 + 12} \\ \\ \sf \implies p = 6.626 \times {10}^{ - 22} \: kg⋅m/s$

$\therefore$

Momentum of X-ray (p) = $\sf 6.626 \times {10}^{ - 22} \: kg⋅m/s$

Answer 2

Answer:

lambda = 10^-12 m

h = 6.626 × 10^-34 kg-m²/s

p = h/lambda

p = 6.626 × 10^-34/10^-12

p = 6.626 × 10^-22 kg-m/s