The wavelength of the first line of Lyman series for hydrogen

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The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen like ion. The atomic number Z of hydrogen like ion is

For first line of Lyman series of hydrogen

	hc	= Rhc		1	-	1
	λ₁			1²		2²

For second line of Balmer series of hydrogen like ion

	hc	= R²hc		1	-	1
	λ₂			2²		4²

By question, λ₁ = λ₂

⇒		1	-	1
		1		2

= Z²		1	-	1		or Z = 2
		4		16