Find the kinetic energy of a neutron with the same wavelength as blue light (λ≈450 nm)

Name: Problem 5, Chapter 6: Modern Physics
Uploaded: 2021-09-24T08:40:53-08:00
Duration: 4 min 40 s
Channel: Devi Dutta Biswajeet
Description: Find the kinetic energy of a neutron with the same wavelength as blue light (λ≈450 nm)

Find the kinetic energy of a neutron with the same...

Key Concepts

Momentum-Kinetic Energy Relationship in Non-Relativistic Mechanics

In non-relativistic mechanics, the kinetic energy (K.E.) of a particle is directly related to its momentum through the relation K.E. = p²/(2m), where m is the mass of the particle. Once the momentum is expressed in terms of the de Broglie wavelength using p = h/?, this formula allows for the computation of kinetic energy directly from the measured or given wavelength.

de Broglie Hypothesis

The de Broglie hypothesis is a cornerstone of quantum mechanics which posits that all matter exhibits wave-like properties. According to this principle, any particle such as a neutron has an associated wavelength given by ? = h/p, where h is Planck’s constant and p is the momentum. This concept provides the foundation for linking the particle's momentum to its wavelength, and is crucial for understanding phenomena where wave-particle duality is observed.

Planck's Constant

Planck’s constant (h) is a fundamental physical constant that plays a key role in quantum mechanics. It appears in the de Broglie relation and governs the scale at which quantum effects become significant. The constant is essential for converting between classical and quantum descriptions of a particle’s properties, such as relating momentum to wavelength.

Transcript

00:01 So in this particular question, we have to find out the value for kinetic energy of a neutron, right? a neutron with wavelength, same as that of blue light, that is 4 .50 nanometers.

00:12 So to find out the wavelength, we'll be taking the help of d.

00:16 Brogley's wavelength formula, right? so this is d.

00:19 Brogley's wavelength formula, which is given by lambda is equal to h by p.

00:25 Or we can say lambda is equal to h by under root 2 m k right so here m is the mass of neutron and k is the kinetic energy of the neutron so in this particular question we have to find the kinetic energy so let me define all the terms first p is basically momentum right will not be using this p value in this particular question rather we will be finding out the value of kinetic energy which is given by k rest all the values are constant values.

00:56 The first constant is our mass of neutron, right? this is mass of neutron.

01:01 Let me represent neutron by n.

01:04 And this is basically planks constant.

01:07 Now planks constant is the very popular constant which has a value of 6 .626 into 10 to power minus 34 jule second.

01:15 So everything here i have converted to si.

01:18 And let me also write the value of lambda here.

01:21 Lambda is 450 nanometers.

01:24 So let us convert that to 2 to si so 450 into 10 to the power minus 9 of a meter right now we are ready to plug in all the values and find k because everything else is known to us h is known 2 is known m is known lambda is known so we have to just find out the value of k so i'm plugging in all the values so our equation will now look like 450 into 10 to the power minus 9 is equal to right so h h, the value of h, is 6 .626 into 10 to the power minus 34...

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