Question

Using the know values of Hydrogen atom.

Calculate :-
a) Radius of third orbit for Li+
b) Speed of Electron in fourth orbit of He+​

Answer 1

$\huge\underline\purple{\sf ♡Answer:-}$

a) Radius of third orbit for $\large{\sf {Li}^{+}}$ :-

We know that :-

$\huge{♡}$$\large{\boxed{\sf r_{n}={\frac{{n}^{2}}{z}}a_{o}}}$

Here ,

n = orbit

z = atomic number

$\sf{a_{o}}$ = constant

its value is 0.529 angstrom

Given :-

n = 3

z = 3

On Putting value :-

$\large\implies{\sf {\frac{{3}^{2}}{3}}×0.529}$

$\large\implies{\sf 1.58 Angstrom}$

$\huge\red{♡}$$\large\red{\boxed{\sf r_{3}=1.58\:Angstrom}}$

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b) Speed of Electron in 4th orbit of $\sf{{He}^{+}}$

We know that :-

$\huge{♡}$$\large{\boxed{\sf v_{n}={\frac{z}{n}}×v_{o}}}$

Here ,

n = orbit

z = atomic number

$\sf{v_o}$ = constant

its value is $\sf{2.19×{10}^{6}m/s}$

Given :-

n = 4

z = 2

On Putting value :-

$\large\implies{\sf {\frac{2}{4}}×2.19×{10}^{6}m/s}$

$\large\implies{\sf 1.0×{10}^{6}m/s}$

$\huge\red{♡}$$\large\red{\boxed{\sf v_{4}=1.0×{10}^{6}m/s}}$