Question

The principal quantum number 'n' for the stationary state orbit of radius 1.3225 nm is​

Answer 1

Answer:

$\huge\mathbb\green{ANSWER}$

We will solve this question by using the given expression of the radius of the stationary state; it is used for the hydrogen atom and hydrogen-like species. We know Bohr’s theory was valid for hydrogen and similar species. The radius of the orbitals is related to the energy level, a charge of the electron. The a0 is proportionality constant.

Complete Solution :

Now, the expression given in the question is used for the hydrogen atom, and also termed as Bohr’s radius i.e. rn=n2a0

Thus, we will write the expression for the radius of hydrogen-like particles in their stationary state, and it can be written as:

rn=n2a0Z

Here we have n represents the nth

Bohr orbit, Z represents the atomic number, and a0 represents the radius of the first stationary state, that remains the same in each case.

The above equation can be modified to determine the value a0 . The equation is,

a0= rnZn2 (1)

- To determine the value of a0 , the radius of the first stationary state can be calculated for the hydrogen atom. The hydrogen atom has the atomic number ‘Z’ equal to 1 and the atom has the one energy level ( 1s ) . Let's substitute the values in the (1) equation. we have,

a0= rnZn2 = rn(1)(1)2 = rn

Thus, the hydrogen atom a0 is equal to the rn value.

Thus from the Bohr radius equation, the value of a0 can be determined as,

rn = a0 = h24πε04π2mee2 ⇒a0= (1.112×10−10 C2N−1m−2)(6.626×10−34Js)24π2(9.109×10−31kg)(1.602×10−19C)2 = 4.917×10−779.219×10−67=0.529×10−10m

- Where h is the planck's constant 6.626×10−34Js

4πε0 , is a permittivity factor and its value is equal to 1.112×10−10 C2N−1m−2

me , is the mass of an electron 9.109×10−31kg

Charge on the electron is ‘e’ is 1.602×10−19C

- So, we can say that the value of a0 is 0.529×10−10m or in the picometer it is equal to 52.9 pm .

Explanation:

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Answer 2

Answer:

We will solve this question by using the given expression of the radius of the stationary state; it is used for the hydrogen atom and hydrogen-like species. We know Bohr’s theory was valid for hydrogen and similar species. The radius of the orbitals is related to the energy level, a charge of the electron. The a0 is proportionality constant.