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The K base α X-rays of aluminum (Z = 13) and zinc (Z = 30) have wavelengths 887 pm and 146 pm respectively. Use Moseley’s law √v = 𝒶(Z – b) to find the wavelength of the K base α X-ray of iron (Z = 26).

The K base α X-rays of aluminum (Z = 13) and zinc (Z = 30) have wavelengths 887 pm and 146 pm respectively. Use Moseley’s law √v = 𝒶(Z – b) to find the wavelength of the K base α X-ray of iron (Z = 26).

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
8 years ago
λ = 887 pm v = C/λ = 3* 10^8/887 * 10^-12 = 33.82 * 10^16 = 5.815 * 10^8 λ base 2 = 146 pm v = 3* 10^8/146* 10^-12 = 0.2054 * 10^20 = 0.054* 10^18 = 1.4331 * 10^9. We know, √v =a(z - b) ⇒ √5.815 * 1068 = a(13 - b)/√1.4331 * 10^9 = a(30 - b) ⇒ 13 – b/30 – b = 5.815 *10^-1/1.4331 = 0.4057. ⇒ 30 * 0.4057 – 0.4057 b = 13 – b ⇒ 12.171 – 0.4.57 b + b = 13 ⇒ b = 0.829/0.5943 = 1.39491 ⇒ a = 5.815 * 1068/11.33 = 0.51323* 10^8 = 5 *10^7. For ‘Fe’, √v = 5 * 10^7 (26 – 1.39) = 5 * 24.61 * 10^7 = 123.05 * 10^7 c/λ = 15141.3 * 10^14 = λ = 3* 10^8/15141.3 * 10^14 = 0.000198 * 10^-6 m = 198 * 10^12 = 198 pm.

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