Question

Nuclear radius R has a dependence on the mass number (A) as R=1.3×10^(-16) A^(1/3) m.For a nucleus of mass number A=125, obtain the order of magnitude of R expressed in metre?

Answer 1

Answer: -15

Explanation:order of magnitude : it is used scientific notation. if any number X in such a way that X = m × 10^n , where m belongs to then, 10ⁿ is known as order of magnitude.

given, nucleus radius R has a dependence on the mass number (A) as R = 1.3 × 10^-16 × A⅓ m.

for a nucleus of mass number , A = 125

R = 1.3 × 10^-6 × (125)⅓

= 1.3 × 10^-6 × (5³)⅓

= 1.3 × 10^-6 × 5 = 6.5 × 10^-16 m

but we know, 6.5 > √10

so, resolve 6.5 in such a way that it lies between √10/10 to √10.

we see, √10/10 < 0.65 < √10

hence, R = 6.5 × 10^-16 = 0.65 × 10^-15 m

here order of magnitude is 10^-15 or simply it can be written as -15.