The wavelength of the Ka line for an element of atomic number 57 is α. The wavelength of the Ka line for the element of atomic number 29 is b α. Find b.

Question

The wavelength of the Ka line for an element of atomic number 57 is α. The wavelength of the Ka line for the element of atomic number 29 is b α. Find b. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

E=(10.2 eV )(Z-1)2 (h c/λ)=(10.2 eV )(Z-1)2 (λ2/λ1)=((Z1-1)2/(Z2-1)2) ; (λ2/α)=((56)2/(28)2) ⇒ λ2=4 α

Q. The wavelength of the $K_{a}$ line for an element of atomic number $57$ is $α$ . The wavelength of the $K_{a}$ line for the element of atomic number $29$ is $b α$ . Find $b$ .

$E = (10.2 e V) (Z - 1)^{2}$
$\frac{h c}{λ} = (10.2 e V) (Z - 1)^{2}$
$\frac{λ _{2}}{λ _{1}} = \frac{( Z _{1} - 1 ) ^{2}}{( Z _{2} - 1 ) ^{2}}$ ;
$\frac{λ _{2}}{α} = \frac{( 56 ) ^{2}}{( 28 ) ^{2}}$
$\Rightarrow λ_{2} = 4 α$

Q. The wavelength of the Ka​ line for an element of atomic number 57 is α. The wavelength of the Ka​ line for the element of atomic number 29 is bα. Find b.

E=(10.2eV)(Z−1)2 λhc​=(10.2eV)(Z−1)2 λ1​λ2​​=(Z2​−1)2(Z1​−1)2​ ; αλ2​​=(28)2(56)2​ ⇒λ2​=4α

Q. The wavelength of the $K_{a}$ line for an element of atomic number $57$ is $α$ . The wavelength of the $K_{a}$ line for the element of atomic number $29$ is $b α$ . Find $b$ .

$E = (10.2 e V) (Z - 1)^{2}$
$\frac{h c}{λ} = (10.2 e V) (Z - 1)^{2}$
$\frac{λ _{2}}{λ _{1}} = \frac{( Z _{1} - 1 ) ^{2}}{( Z _{2} - 1 ) ^{2}}$ ;
$\frac{λ _{2}}{α} = \frac{( 56 ) ^{2}}{( 28 ) ^{2}}$
$\Rightarrow λ_{2} = 4 α$