Suppose a nucleus of 93X236 fissions into two fragments whose mass ratio is 0.37:0.63. With the aid of the drawing, estimate the energy (in MeV) released during this fission.
Ive treied to do this problem but i keep getting the wrong answer. I keep getting 164.253 MeV
To estimate the energy released during a fission reaction, we can use the concept of the mass defect and Einstein's mass-energy equivalence equation, E = mc^2. Here's how you can calculate it:
1. Determine the mass of the initial nucleus (93X236) and the masses of the two fragments after fission. Let's assume the mass of the initial nucleus (m_initial) is equal to the sum of the masses of the two fragments (m_1 + m_2).
2. Calculate the mass defect (Δm) by subtracting the mass of the initial nucleus from the sum of the masses of the fragments: Δm = m_initial - (m_1 + m_2).
3. Multiply the mass defect by the speed of light squared (c^2) to obtain the energy released: E = Δm * c^2.
Now, let's proceed with the calculations:
1. The mass of the initial nucleus, 93X236, can be obtained from a standard periodic table. For uranium-236, you can find the atomic mass as 236 atomic mass units (u).
2. The mass ratio of the fragments is given as 0.37:0.63. Let's assume the mass of fragment 1 (m_1) is 0.37x and the mass of fragment 2 (m_2) is 0.63x, where x is the total mass of the initial nucleus, 236u.
m_1 = 0.37x
m_2 = 0.63x
3. Calculate the total mass of the fragments:
m_initial = m_1 + m_2
236u = 0.37x + 0.63x
Solve for x:
236u = x
Therefore, the masses of the fragments are:
m_1 = 0.37 * 236u = 87.32u
m_2 = 0.63 * 236u = 148.68u
4. Calculate the mass defect:
Δm = m_initial - (m_1 + m_2)
= 236u - (87.32u + 148.68u)
= -0.04u
5. Use the mass-energy equivalence equation to calculate the energy released:
E = Δm * c^2 = -0.04u * (3.00 × 10^8 m/s)^2 = -3.60 × 10^13 J
To convert the energy from joules (J) to megaelectronvolts (MeV), we divide by the conversion factor: 1 MeV = 1.60218 × 10^-13 J.
E = -3.60 × 10^13 J / (1.60218 × 10^-13 J/MeV) = -224.67 MeV
The negative sign indicates that energy is released during the fission reaction. Therefore, the estimated energy released during this fission is approximately 224.67 MeV.
It seems the answer you obtained, 164.253 MeV, is incorrect. Please double-check your calculations or ensure that you followed the steps correctly.