A beam of neutrons (mneutron = 1.6749 x 10^-24 g) has a velocity of 1.44 km/hour. What is the wavelength of
the neutron wave?
The answer is 993 nm.
I tried to use 1/2mv^2=hc/lambda but I got 1483.5 m
You are using the wrong equation. Yours says that the kinetic energy equals the photon energy. A neutron is not a photon.
The De Broglie wavelength of a matter wave, which is what this is, is
Lambda = h/(momentum), where h is Planck's constant
Make sure you convert 1.44 km/hr to 0.400 m/s
Momentum = 6.7*10^-28 kg m/s
h = 6.62*10^-34 J s
lambda = 6.62*10^-34 J/s / 6.7*10^-28 kg m/s = ? (it will agree with the answer)
Ooh I forgot about that one. thank you
To find the wavelength of the neutron wave, you can use the de Broglie equation, which relates the wavelength of a particle to its momentum. The de Broglie equation is given by:
λ = h / p
where λ is the wavelength, h is the Planck's constant (6.626 x 10^-34 J·s), and p is the momentum of the particle.
To determine the momentum of the neutron, you need to find its mass and velocity first. The mass of the neutron is given as:
m_neutron = 1.6749 x 10^-24 g
Next, you need to convert the velocity from km/h to m/s:
v = 1.44 km/hour = 1.44 * 1000 / 3600 m/s ≈ 0.4 m/s
Now, you can calculate the momentum of the neutron:
p = m * v
p = (1.6749 x 10^-24 g) * 0.4 m/s
To convert the mass from grams to kilograms, divide by 1000:
p = (1.6749 x 10^-27 kg) * 0.4 m/s
Now, substitute the values of h and p into the de Broglie equation:
λ = (6.626 x 10^-34 J·s) / (1.6749 x 10^-27 kg) * 0.4 m/s
Simplifying the equation:
λ ≈ 9.93 x 10^-10 m
Converting meters to nanometers:
λ ≈ 993 nm
So, the wavelength of the neutron wave is approximately 993 nm.
To find the wavelength of the neutron wave, you can use the de Broglie equation, which relates the wavelength of a particle to its momentum.
The de Broglie equation is given by:
λ = h / p
Where:
λ is the wavelength of the particle
h is Planck's constant (h = 6.626 x 10^-34 J·s)
p is the momentum of the particle
To calculate the momentum of the neutron, you can use its mass and velocity. The momentum of an object is defined as the product of its mass and velocity:
p = m * v
Where:
p is the momentum
m is the mass of the neutron
v is the velocity of the neutron
Given:
Mass of the neutron (mneutron) = 1.6749 x 10^-24 g (or you can convert it to kg: mneutron = 1.6749 x 10^-27 kg)
Velocity of the neutron (v) = 1.44 km/hour
First, let's convert the velocity from km/hour to m/s, to ensure the units are consistent. We know that 1 km = 1000 m and 1 hour = 3600 seconds.
v = (1.44 km/hour) * (1000 m/km) / (3600 s/hour)
v = 0.4 m/s
Next, calculate the momentum of the neutron:
p = (1.6749 x 10^-27 kg) * (0.4 m/s)
p = 6.6996 x 10^-28 kg·m/s
Now, substitute the values of h and p into the de Broglie equation to find the wavelength:
λ = (6.626 x 10^-34 J·s) / (6.6996 x 10^-28 kg·m/s)
λ = 9.895 x 10^-7 m
Finally, to convert the wavelength from meters to nanometers, multiply by 10^9:
λ = 9.895 x 10^-7 m * 10^9 nm/m
λ = 989.5 nm
So the wavelength of the neutron wave is approximately 989.5 nm.