If the wave number of first line of Balmer series of H-atom is ' x ' then the wave number of first line of Lyman series of the He +ion will be expressed as Z × x. Find the value of Z?

Question

If the wave number of first line of Balmer series of H-atom is ' x ' then the wave number of first line of Lyman series of the He +ion will be expressed as Z × x. Find the value of Z? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

overline V =R Z2((1/n12)-(1/n22)) x=R((1/22)-(1/32))=(5 R/36) barv1=R × 22(1-(1/22))=3 R =(36/5) x × 3=(108 x/5)

Q. If the wave number of first line of Balmer series of $H$ -atom is ' $x$ ' then the wave number of first line of Lyman series of the $H e^{+}$ ion will be expressed as $Z \times x$ . Find the value of $Z$ ?

$\overline{V} = R Z^{2} (\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}})$
$x = R (\frac{1}{2 ^{2}} - \frac{1}{3 ^{2}}) = \frac{5 R}{36}$
$\overset{v}{ˉ}_{1} = R \times 2^{2} (1 - \frac{1}{2 ^{2}}) = 3 R$
$= \frac{36}{5} x \times 3 = \frac{108 x}{5}$

Q. If the wave number of first line of Balmer series of H-atom is ' x ' then the wave number of first line of Lyman series of the He+ion will be expressed as Z×x. Find the value of Z?

V=RZ2(n12​1​−n22​1​) x=R(221​−321​)=365R​ vˉ1​=R×22(1−221​)=3R =536​x×3=5108x​

Q. If the wave number of first line of Balmer series of $H$ -atom is ' $x$ ' then the wave number of first line of Lyman series of the $H e^{+}$ ion will be expressed as $Z \times x$ . Find the value of $Z$ ?

$\overline{V} = R Z^{2} (\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}})$
$x = R (\frac{1}{2 ^{2}} - \frac{1}{3 ^{2}}) = \frac{5 R}{36}$
$\overset{v}{ˉ}_{1} = R \times 2^{2} (1 - \frac{1}{2 ^{2}}) = 3 R$
$= \frac{36}{5} x \times 3 = \frac{108 x}{5}$