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

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 $\left[\frac{\sqrt{10}}{10},\sqrt{10}\right]$ 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.

Answer 2

Answer:

Order, -15

Explanation:

It is given that,

The nuclear radius R depends on the mass number as :

$R=1.3\times 10^{-16} A^{1/3}$

A is the mass number of the atom

Here, A = 125

Use A in above formula as :

$R=1.3\times 10^{-16} (125)^{1/3}$

$R=6.5\times 10^{-16}$

or

$R=0.65\times 10^{-15}$

It is clear from the above value that the order of the nuclear radius is (-15). Hence, this is the required solution.