Calculate Max Kinetic Energy of Neutron in MeV, Physics Book Error?

[Ry122]

I think there was a an error made in my physics book.
It says alpha particles are fired at beyllium nuclei to induce the reaction
Be He C + n
Calculate the maximum kinetic energy of the neutron in MeV.
Im guessing it means Be + He = C + n
This makes the atomic numbers and mass numbers on the left equal to the ones on the right side. I am unsure if this is correct through because isn't the left side only supposed to have the atom that was fired at?

 

[mgb_phys]

The left side is what you start with, the right side is what it turns into.
SO Be + He = C + n is correct.
If you should write He as a chemical reaction for a process involving an alpha particle is probably something for the chemists to argue about.

 

[ogb p]

Thank you for bringing this potential error to my attention. After reviewing the reaction, I can confirm that the left side should only have the atoms that were fired at (Be and He), while the right side should have the resulting products (C and n). This means that the equation should be written as Be + He --> C + n.

To calculate the maximum kinetic energy of the neutron, we can use the conservation of energy principle, where the total energy before and after the reaction must be equal. This can be expressed as:

E_initial = E_final

Where E_initial is the energy of the alpha particles (Be and He) and E_final is the energy of the resulting products (C and n). We can express the energy of a particle using the famous equation E=mc^2, where m is the mass and c is the speed of light.

Since we are interested in the kinetic energy of the neutron, we can use the equation K.E. = (1/2)mv^2, where m is the mass and v is the speed of the particle.

To find the maximum kinetic energy, we need to find the minimum mass of the neutron. According to the atomic mass table, the mass of a neutron is approximately 1.008665 amu (atomic mass units).

Now, using the conservation of energy principle, we can set up the following equation:

E_initial = E_final
(m_Be + m_He)c^2 = (m_C + m_n)c^2 + K.E_n

Where m_Be and m_He are the masses of Be and He, and m_C and m_n are the masses of C and n respectively.

Substituting the known values, we get:

(9.012182 + 4.002602)c^2 = (12 + 1.008665)c^2 + K.E_n

Solving for K.E_n, we get:

K.E_n = (9.012182 + 4.002602 - 12 - 1.008665)c^2
= (0.006119)c^2

Using the value of c (speed of light) in MeV, which is approximately 2.998 x 10^8 m/s, we get:

K.E_n = (0.006119)(2.998 x 10^8)^2
= 5.512 MeV

Therefore, the maximum kinetic energy of the neutron