An example of the neutron absorption reaction is .
1 0 n+10 5 B-->7 3 Li+ 4 2 He
The rest masses of each particle in atomic mass units (u) are
1 0 n= 1 u
10 5 B=10 u
7 3 Li =7 u
4 2 He= 4 u
where 1u=1.66x10^-27 kg.
calculate Q
Q= in MeV
I have the same question please someone help me solve this. Thank you
¹₀n+¹º₅B = ⁷₃Li+⁴₂He
Δm = m(¹₀n) + m(¹º₅B) – m(⁷₃Li)-m(⁴₂He)=
=1.009 + 10.811 – 6.941 – 4.003 = 0.876 u.
ΔE=mc²=0.876 •1.66•10⁻²⁷•9•10¹⁶ =
=1.31•10⁻¹º J= =8.18•10⁸ eV =818 MeV
Hi Elena thank you so much for your help but this answer is wrong i don't know why. Maybe because c is squared and did you squared c ? Please help me out
To calculate the Q value for the given neutron absorption reaction, we need to compute the mass difference between the reactants and the products. The equation for the Q value is:
Q = (m_initial - m_final) * c^2
where m_initial is the total initial mass of the reactants, m_final is the total final mass of the products, and c is the speed of light.
Let's calculate the Q value step-by-step:
Step 1: Convert the masses from atomic mass units (u) to kilograms (kg):
1 u = 1.66 x 10^-27 kg
The masses in kg are:
m_initial = (1 u + 10 u) * (1.66 x 10^-27 kg/u) = 16.6 x 10^-27 kg
m_final = (7 u + 4 u) * (1.66 x 10^-27 kg/u) = 13.98 x 10^-27 kg
Step 2: Calculate the mass difference:
Δm = m_initial - m_final = (16.6 - 13.98) x 10^-27 kg = 2.62 x 10^-27 kg
Step 3: Convert the mass difference to energy using Einstein's mass-energy equivalence equation:
E = Δm * c^2
Since E is in joules (J), we need to convert c from m/s to m^2/s^2 by squaring it.
c = 299,792,458 m/s
c^2 = (299,792,458 m/s)^2 = 8.99 x 10^16 m^2/s^2
E = (2.62 x 10^-27 kg) * (8.99 x 10^16 m^2/s^2) = 2.36 x 10^-10 J
Step 4: Convert the energy from joules to megaelectronvolts (MeV):
1 MeV = 1.6 x 10^-13 J
Q = E / (1.6 x 10^-13 J/MeV) = 2.36 x 10^-10 J / (1.6 x 10^-13 J/MeV) = 1475 MeV
Therefore, the Q value for the neutron absorption reaction is 1475 MeV.
To calculate Q for a nuclear reaction, you need to determine the difference in mass between the initial particles (reactants) and the final particles (products). The Q value represents the energy released or absorbed during the reaction.
In this case, you have the following reaction:
1 0 n + 10 5 B → 7 3 Li + 4 2 He
To calculate Q, you need to find the mass difference between the initial and final particles:
Mass of reactants = Mass of neutron (1u) + Mass of Beryllium-10 (10u) = 1u + 10u = 11u
Mass of products = Mass of Lithium-7 (7u) + Mass of Helium-4 (4u) = 7u + 4u = 11u
Now, find the mass difference:
Δm = Mass of reactants - Mass of products = 11u - 11u = 0u
Note: The mass difference is zero in this case.
To calculate the energy released or absorbed (Q) during the reaction, you can use Einstein's mass-energy equivalence equation:
E = Δm * c^2
Where:
E is the energy released or absorbed (in joules)
Δm is the mass difference
c is the speed of light (approximately 3.0 x 10^8 m/s)
To convert the energy to MeV, you can use the conversion factor:
1 MeV = 1.6 x 10^-13 J
So, the equation becomes:
Q (in MeV) = (Δm * c^2) / (1.6 x 10^-13)
Since the mass difference (Δm) is zero in this case, the energy released (Q) will also be zero.