To find the velocity of the particle of mass 2 mg that has the same wavelength as a neutron moving with a velocity of
3×105ms−1, we can use the de Broglie wavelength formula:
λ=‌Where:
λ is the wavelength
h is Planck's constant (approximately
6.626×10−34‌Js )
m is the mass of the particle
v is the velocity of the particle
First, let's find the wavelength of the neutron. The mass of the neutron is given as
1.67×10−27‌Kg and its velocity is
3×105ms−1.
Plugging in the values:
λ=‌| 6.626×10−34 |
| 1.67×10−27⋅3×105 |
Let's calculate this:
‌λ=‌| 6.626×10−34 |
| 5.01×10−22 |
‌λ≈1.322×10−12m Since the particle of mass 2 mg has the same wavelength, we can use this value to find its velocity. The mass of the particle is:
m‌particle ‌=2‌mg=2×10−3g=2×10−6‌KgNow, using the de Broglie formula again:
v‌particle ‌=‌Plugging in the values:
v‌particle ‌=‌| 6.626×10−34 |
| 1.322×10−12⋅2×10−6 |
Let's calculate this:
‌v‌particle ‌=‌| 6.626×10−34 |
| 2.644×10−18 |
‌v‌particle ‌≈2.507×10−16ms−1v‌particle ‌=‌| 6.626×10−34 |
| 1.322×10−12⋅2×10−6 |
Let's calculate this:
‌v‌particle ‌=‌| 6.626×10−34 |
| 2.644×10−18 |
‌v‌particle ‌≈2.507×10−16ms−1 Thus, the velocity of the particle is approximately
2.5×10−16ms−1, which corresponds to option A.
Option A:
2.5×10−16ms−1