JEE MAIN - Physics (2025 - 23rd January Morning Shift - No. 4)
Explanation
To find the matter wave behavior of the particle, we use the de Broglie wavelength formula:
$$\lambda = \frac{h}{mv}$$
where:
$$h = 6.63 \times 10^{-34} \, \mathrm{J \cdot s}$$ is Planck’s constant,
$$m = 10^{-30} \, \mathrm{kg}$$ is the mass of the particle, and
$$v = 2.21 \times 10^6 \, \mathrm{m/s}$$ is its velocity.
Follow these steps:
Substitute the values into the formula:
$$\lambda = \frac{6.63 \times 10^{-34}}{(10^{-30})(2.21 \times 10^6)}$$
Calculate the denominator:
$$10^{-30} \times 2.21 \times 10^6 = 2.21 \times 10^{-24}$$
Now compute the wavelength:
$$\lambda \approx \frac{6.63 \times 10^{-34}}{2.21 \times 10^{-24}} \approx 3 \times 10^{-10} \, \mathrm{m}$$
This wavelength, roughly $$3 \times 10^{-10} \, \mathrm{m}$$ (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.
Comments (0)
