The wavelengths of K _ X -rays for lead isotopes Pb ²⁰⁸, ~Pb ²⁰⁶ and Pb ²⁰⁴ are ₁, ₂ and ₃ respectively. Then

Step-by-step solution

Wavelengths of the K_ lines for given isotopes of lead ( Pb ) can be given by a general expression 1 =R(Z-1)^2 ( 1 1^2 - 1 2^2 ) where R= Rydberg's constant, Z= atomic number of the isotopes. Though Pb ²⁰⁸, ~Pb ²⁰⁶ and Pb ²⁰⁴ have different atomic masses, Z will be same for them i.e. 82 . aligned & 1 ₁ =R(82-1)^2 ( 1 1^2 - 1 2^2 )= 3 4 R(81)^2 & 1 ₂ = 3 4 R (81^2 ) and 1 ₃ = 3 4 R (81^2 ) & ( 1 ₂ )^2= 1 ₁ 1 ₃ ₂= ₁ ₃ aligned