determine the velocity and kinetic energy of neutrons having de broglie wave length 1 angstrom
Lambda=h/mv
v=lambda.m/h
and KE=mv^2/2.
Lambda(wavelength) is given. So substitute it and do the calculation.
Thnx
To determine the velocity and kinetic energy of neutrons with a De Broglie wavelength of 1 angstrom, we can use the De Broglie equation and the equation for kinetic energy.
1. De Broglie equation:
λ = h / p
Where:
λ is the De Broglie wavelength (given as 1 Å = 1 x 10^-10 m)
h is Planck's constant (h = 6.62607015 × 10^-34 J·s)
p is the momentum of the neutron
2. Momentum:
p = m * v
Where:
p is the momentum
m is the mass of the neutron (m = 1.675 × 10^-27 kg)
v is the velocity of the neutron
3. Rearrange the De Broglie equation to solve for momentum:
p = h / λ
Substituting the given values:
p = (6.62607015 × 10^-34 J·s) / (1 x 10^-10 m)
p = 6.62607015 × 10^-24 kg·m/s
4. Use the momentum equation to solve for velocity:
v = p / m
Substituting the values:
v = (6.62607015 × 10^-24 kg·m/s) / (1.675 × 10^-27 kg)
v = 3944.46 m/s
5. Kinetic Energy:
KE = (1/2) * m * v^2
Substituting the values:
KE = (1/2) * (1.675 × 10^-27 kg) * (3944.46 m/s)^2
KE = 5.88 × 10^-21 J
Therefore, the velocity of the neutrons is approximately 3944.46 m/s, and the kinetic energy is approximately 5.88 × 10^-21 J.
To determine the velocity and kinetic energy of neutrons with a given de Broglie wavelength, we can use the de Broglie equation and the mass of a neutron.
The de Broglie equation states: λ = h / mv
where:
- λ is the de Broglie wavelength (given as 1 angstrom or 1 x 10^-10 meters)
- h is the Planck's constant (6.626 x 10^-34 J*s)
- m is the mass of the neutron (approximately 1.67493 x 10^-27 kg)
- v is the velocity we are trying to find
First, rearrange the equation to solve for v:
v = h / (m * λ)
Substitute the values:
v = (6.626 x 10^-34 J*s) / (1.67493 x 10^-27 kg * 1 x 10^-10 m)
Now calculate the velocity:
v ≈ 3.950 x 10^2 m/s
To calculate the kinetic energy (KE) of the neutron, we can use the formula:
KE = (1/2) * m * v^2
Substitute the mass of the neutron (m) and the velocity (v) we just found:
KE = (1/2) * (1.67493 x 10^-27 kg) * (3.950 x 10^2 m/s)^2
Now calculate the kinetic energy:
KE ≈ 1.314 x 10^-22 J
Therefore, the velocity of neutrons with a de Broglie wavelength of 1 angstrom is approximately 3.950 x 10^2 m/s, and the corresponding kinetic energy is about 1.314 x 10^-22 J.