Find the mass number of an atom whose radius is half of that of a given atom of mass number 192.

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4 months ago

r = R 0 ( 1 9 2 ) 1 3

r 2 = R 0 ( m ) 1 3

m = 1 9 2 8 = 2 4

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A = A 0 e λ t 1     [Radio active decay law]

A 5 = A 0 e λ ( t 2 t 1 )

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f o r A , t 1 2 = 4 s e c  

= m A 0 e 0 . 6 9 3 4 × 1 6

m A = m A 0 e 4 × 0 . 6 9 3    -(1)

for B,

for B,  t 1 2 = 8 s e c  

m B = m B 0 e 2 × 0 . 6 9 3               -(2)

m A m B = m A O m B O e 4 × 0 . 6 9 3 e 2 × 0 . 6 9 3

m A m B = 2 5 1 0 0 = x 1 0 0 x = 2 5

The reaction is X²? → Y¹²? + Z¹²?
Binding energies per nucleon are: X=7.6 MeV, Y=8.5 MeV, Z=8.5 MeV.
Gain in binding energy (Q) = (Binding energy of products) - (Binding energy of reactants)
Q = (120 × 8.5 + 120 × 8.5) - (240 × 7.6) MeV
Q = (2 × 120 × 8.5) - (240 × 7.6) MeV = 2040 - 1824 = 216 MeV.

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Physics Ncert Solutions Class 12th 2023

Physics Ncert Solutions Class 12th 2023

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