Question 79: Dual Nature of Matter and Radiation

Question

A sub-atomic particle of mass $10^{-30} \mathrm{~kg}$ is moving with a velocity $2.21 	imes 10^6 \mathrm{~m} / \mathrm{s}$. Under the matter wave consideration, the particle will behave closely like $\qquad$ $\left(\mathrm{h}=6.63 	imes 10^{-34} \mathrm{~J} . \mathrm{s}ight)$

Accepted Answer

To find the matter wave behavior of the particle, we use the de Broglie wavelength formula:
$$\lambda = \frac{h}{mv}$$
where:
$$h = 6.63 	imes 10^{-34} \, \mathrm{J \cdot s}$$ is PlanckÃ¢ÂÂs constant,
$$m = 10^{-30} \, \mathrm{kg}$$ is the mass of the particle, and
$$v = 2.21 	imes 10^6 \, \mathrm{m/s}$$ is its velocity.
Follow these steps:
Substitute the values into the formula:
$$\lambda = \frac{6.63 	imes 10^{-34}}{(10^{-30})(2.21 	imes 10^6)}$$
Calculate the denominator:
$$10^{-30} 	imes 2.21 	imes 10^6 = 2.21 	imes 10^{-24}$$
Now compute the wavelength:
$$\lambda \approx \frac{6.63 	imes 10^{-34}}{2.21 	imes 10^{-24}} \approx 3 	imes 10^{-10} \, \mathrm{m}$$
This wavelength, roughly $$3 	imes 10^{-10} \, \mathrm{m}$$ (or 0.3 nm), lies within the X-ray portion of the electromagnetic spectrum, since X-rays typically have wavelengths in the range of about 0.01 nm to 10 nm.
Therefore, under the matter wave consideration, the particle will behave closely like:
Option A: X-rays.

Answer

X-rays

Answer

Infra-red radiation

Answer

Gamma rays

Answer

Visible radiation

Dual Nature of Matter and Radiation

A sub-atomic particle of mass 10^{-30} \mathrm{~kg} is moving with a velocity 2.21 \times 10^6 \mathrm{~m} / \mathrm{s}. Under the matter wave consideration, the particle will behave closely like \qquad \left(\mathrm{h}=6.63 \times 10^{-34} \mathrm{~J} . \mathrm{s}\right)

Choose the correct answer: