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NEET PHYSICSEasy

The radius of inner most orbit of hydrogen atom is 5.3×10−11 m5.3 \times 10^{-11} \text{ m}. What is the radius of third allowed orbit of hydrogen atom?

1

0.53 A˚0.53 \text{ } \text{\AA}

2

1.06 A˚1.06 \text{ } \text{\AA}

3

1.59 A˚1.59 \text{ } \text{\AA}

4

4.77 A˚4.77 \text{ } \text{\AA}

Step-by-Step Solution

The radius of the nn-th orbit of a hydrogen atom is given by rn=n2r1r_n = n^2 r_1, where r1=5.3×10−11 m=0.53 A˚r_1 = 5.3 \times 10^{-11} \text{ m} = 0.53 \text{ } \text{\AA}. For the third orbit, n=3n = 3, so r3=32×0.53 A˚=9×0.53 A˚=4.77 A˚r_3 = 3^2 \times 0.53 \text{ } \text{\AA} = 9 \times 0.53 \text{ } \text{\AA} = 4.77 \text{ } \text{\AA}.

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