The binding energy per nucleon of ${}_{8}^{16}O$ is 7.97 MeV and that of O¹⁷ is 7.75 MeV. Calculate the energy required to remove a neutron from ${}_{8}^{17}O .$

Name: Wired Faculty - The Best Learning App
Rating: 4.6 (1864 reviews)

Solution

The nuclear reaction is represented as follow:

{}_{8}^{17}O \to {}_{8}^{16}O + {}_{0}^{1}n

B.E per nucleon of

{}_{8}^{16}O

= 7.97 MeV

B.E per nucleon of O¹⁷ = 7.75 MeV

Energy required to remove a neutron from

{}_{8}^{17}O

= ?

If m_p represents the mass of a proton and m_n that of a neutron, the energy required to remove a neutron from

{}_{8}^{17}O

is given by,

E = energy equivalent of (mass of {}_{8}^{16}O + m_{n} - mass of {}_{8}^{17}O)

= (8 m_{p} + 8 m_{n} - 7.97 \times 16) + m_{n} - (8 m_{p} + 9 m_{n} - 7.75 \times 17)

= [7.75 \times 17 - 7.97 \times 16] MeV = 4.23 MeV .

For Daily Free Study Material Join wiredfaculty