Question

# The each revolves round the sun due to gravit ational attraction. Suppose that the sun and the earth are point particles with their existing mas ses and that Bohr's quantization rule for angular momentum is vaild case of gravitation.  (a) Calculate the minimum  radius the earth can have for its orbit.  (b) What is value of the principal quantum num ber n for the present radius ? Mass of the earth  =  6.0×1024  kg, Mass of the sun = 2.0×1030  kg, earth-sun distance =  1.5×1011 m.

Solution

## Mass of Earth = Me=6.0×1024  kg Mass of Sun =  M8=2.0×1030   kg Earth- Sun distance = 1.5×1011  m Since        mvr =  nh2π or,      m2v2r2=n2h22π2.....(1)  GMeM8r2=Mev2r or    v2=GM8r              ...............(2) Dividing (1) and (2) We get     M2er=n2h24π2GM8 for n = 1,  r =  √h2402GM8M2e = √(6.6×10−24)24×(3.14)2×6.67×10−11×(6×1024)×2×1030 =  2.29×10−138m =  2.3×10138m (b)   n2 =  M2e×r×4×π2×G×M8h2  (6×1024)2×1.5×1011×4×(3.14)2×6.67×10−11×2×1030(6.6×10−34)2 =  2.5×1074

Suggest corrections

0 Upvotes

Similar questions
View More

Same exercise questions
View More

People also searched for
View More