Question #199665

a) Calculate the distance travelled by an electron when it moves form 1st shell to 3rd shell of hydrogen atom.

b) Also calculate the amount of energy needed to send the electron from 1st to 3rd shell of hydrogen atom.

This question is a must attempt so plz answer it. Much appreciated.

Expert's answer

Distance can be calculated by formula of radius -

a)

Formula of bohr's radius when electron is in 1st shell is given by -

Let it be denoted by "r_1" "=0.529" "\\dfrac{n^{2}}{Z}\\ A^{0}"

For hydrogen atom Z=1 , first shell means that n=1 ,

"r_{1}=0.529\\dfrac{n^{2}}{1}"

"r_1=0.529\\ A^{0}"

Formula of bohr's radius when electron is in 3rd shell is given by -

Let it is denoted by "r_3=0.529\\dfrac{n^{2}}{Z}\\ A^{0}"

"r_3=" "4.761A^{0}"

Distance can be calculated as = "r_{3}-r_{1}=4.761-0.529=4.232A^{O}"

B) Formula of energy is given by-

"E_{n}=-\\dfrac{13.6}{n^{2}}"

for n=1 , we get -

"E_{1}=-13.6"

for n=3 , we get -

"E_3=-\\dfrac{13.6}{9}=-1.511"

now "\\Delta{E}=E_3-E_1=-1.511+13.6=12.089\\ ev"

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