The radii of the first,second,third,and fourt | vedclass

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(A) The radius of the $n^{th}$ Bohr orbit for a hydrogen-like atom is given by the formula $r_n = 0.529 	imes \frac{n^2}{Z} \,\ \mathring{A}$.
For h

Vedclass · Accepted Answer

$0.529 \,\mathring{A}, 2.116 \,\mathring{A}, 4.761 \,\mathring{A}, 8.464 \,\mathring{A}$

Vedclass · Answer

(A) The radius of the $n^{th}$ Bohr orbit for a hydrogen-like atom is given by the formula $r_n = 0.529 	imes \frac{n^2}{Z} \,\ \mathring{A}$.
For hydrogen,the atomic number $Z = 1$,so the formula simplifies to $r_n = 0.529 	imes n^2 \,\mathring{A}$.
For $n = 1$: $r_1 = 0.529 	imes 1^2 = 0.529 \,\mathring{A}$.
For $n = 2$: $r_2 = 0.529 	imes 2^2 = 0.529 	imes 4 = 2.116 \,\mathring{A}$.
For $n = 3$: $r_3 = 0.529 	imes 3^2 = 0.529 	imes 9 = 4.761 \,\mathring{A}$.
For $n = 4$: $r_4 = 0.529 	imes 4^2 = 0.529 	imes 16 = 8.464 \,\mathring{A}$.
Thus,the radii are $0.529 \,\mathring{A}, 2.116 \,\mathring{A}, 4.761 \,\mathring{A}, 8.464 \,\mathring{A}$.

The radii of the first,second,third,and fourth Bohr orbits of hydrogen are respectively:

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