An alpha particle (4He)has a mass of 4.00300 amu. A proton has mass of 1.00783 amu and a neutron has mass of 1.00867 amu respectively. The binding energy of alpha particle estimated from these data is the closest to

Question

An alpha particle (4He)has a mass of 4.00300 amu. A proton has mass of 1.00783 amu and a neutron has mass of 1.00867 amu respectively. The binding energy of alpha particle estimated from these data is the closest to (A) 27.9 MeV (B) 22.3 MeV (C) 35.0 MeV (D) 20.4 MeV

Tardigrade Admin · Accepted Answer

The mass defect, Δ m=2(mp+mn)-m He =2(1.00783+1.00867)-4.00300 =0.0300 amu So, the binding energy, E=Δ m c2 =0.03 × 931 MeV ≈ 27.9 MeV

Q. An alpha particle (⁴He)has a mass of 4.00300 amu. A proton has mass of 1.00783 amu and a neutron has mass of 1.00867 amu respectively. The binding energy of alpha particle estimated from these data is the closest to

27.9 MeV

22.3 MeV

35.0 MeV

20.4 MeV

The mass defect, $Δ m = 2 (m_{p} + m_{n}) - m_{He}$
$= 2 (1.00783 + 1.00867) - 4.00300$
$= 0.0300$ amu
So, the binding energy, $E = Δ m c^{2}$
$= 0.03 \times 931 M e V \approx 27.9 M e V$

Q. An alpha particle (4He)has a mass of 4.00300 amu. A proton has mass of 1.00783 amu and a neutron has mass of 1.00867 amu respectively. The binding energy of alpha particle estimated from these data is the closest to