Moseley's law for Kα photon is given by √v=a(Z-b) where a is a universal constant and b is a screening constant. Moseley's logic helps us assume b=1 for Kα photon. If there is a percentage error =10-2 in the measurement of b due to actual orbital configuration of an atom, then the relative error in the measurement of v if Z=51 is p × 10-q. Find the value of (p q).

Question

Moseley's law for Kα photon is given by √v=a(Z-b) where a is a universal constant and b is a screening constant. Moseley's logic helps us assume b=1 for Kα photon. If there is a percentage error =10-2 in the measurement of b due to actual orbital configuration of an atom, then the relative error in the measurement of v if Z=51 is p × 10-q. Find the value of (p q). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

(d b/b)=10-4 ⇒ d b=10-4 (1/2) (d v/v)=(d(Z-b)/(Z-b)) ⇒ (d v/v)=(2 × 10-4/50) =4 × 10-6

bdb​=10−4 ⇒db=10−4 21​vdv​=(Z−b)d(Z−b)​ ⇒vdv​=502×10−4​ =4×10−6

$\frac{d b}{b} = 1 0^{- 4}$
$\Rightarrow d b = 1 0^{- 4}$
$\frac{1}{2} \frac{d v}{v} = \frac{d ( Z - b )}{( Z - b )}$
$\Rightarrow \frac{d v}{v} = \frac{2 \times 1 0 ^{- 4}}{50}$
$= 4 \times 1 0^{- 6}$