If the lowest energy x -rays have λ=4.0 × 10-8 m , at what z (minimum) would a transition from the second energy level to the first result in the emission of X-ray?

Question

If the lowest energy x -rays have λ=4.0 × 10-8 m , at what z (minimum) would a transition from the second energy level to the first result in the emission of X-ray? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

λ=4 × 10-8 m =400 mathringA, energy of photon =(12375/λ) eV So ; (12375/400)=13.6 Z 2(1-(1/4)) ⇒ Z2=3.04 ⇒ Z=1.74 ∼ 2 (Helium)

Q. If the lowest energy $x$ -rays have $λ = 4.0 \times 1 0^{- 8} m,$ at what $z$ (minimum) would a transition from the second energy level to the first result in the emission of X-ray?

$λ = 4 \times 1 0^{- 8} m = 400 \overset{˚}{A}$ ,

energy of photon $= \frac{12375}{λ} e V$

So ; $\frac{12375}{400} = 13.6 Z^{2} (1 - \frac{1}{4})$

$\Rightarrow Z^{2} = 3.04$

$\Rightarrow Z = 1.74 \sim 2$ (Helium)

Q. If the lowest energy x -rays have λ=4.0×10−8m, at what z (minimum) would a transition from the second energy level to the first result in the emission of X-ray?

λ=4×10−8m=400A˚, energy of photon =λ12375​eV So ; 40012375​=13.6Z2(1−41​) ⇒Z2=3.04 ⇒Z=1.74∼2 (Helium)

Q. If the lowest energy $x$ -rays have $λ = 4.0 \times 1 0^{- 8} m,$ at what $z$ (minimum) would a transition from the second energy level to the first result in the emission of X-ray?

$λ = 4 \times 1 0^{- 8} m = 400 \overset{˚}{A}$ ,

energy of photon $= \frac{12375}{λ} e V$

So ; $\frac{12375}{400} = 13.6 Z^{2} (1 - \frac{1}{4})$

$\Rightarrow Z^{2} = 3.04$

$\Rightarrow Z = 1.74 \sim 2$ (Helium)