A silver atom in a solid oscillaties in simple harmonic motion in some direction with frequency of `10^((12)"/"sec)`. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 and Avagardo number `=6.02xx 10^(23)g m "mole"^(-1)`).

Options

A. `6.4 N"/"m`
B. `7.1 N"/"m`
C. `2.2N"/"m`
D. `5.5 N"/"m`

Answer

B

Explanation

Time period of SHM `T= 2pi sqrt((m)/(k))`
Frequency `f= (1)/(2pi) sqrt((k)/(m))`
`therefore f^(2)= (k)/(4pi^(2) m)" ""……."(1)`
Now, the mass of one atom of silver
`m= (M)/(N_A)xx 10^(-3)kg`
`= (108)/(6.02xx10^(23))xx10^(-3)`
`=17.94 xx 10^(-26)`
From equation (1),
`therefore 10^(24)= (k)/(4xx (3.14)^(2)xx 17.94xx 10^(-26))`
`therefore k= 4xx 9.8596xx 17.94xx 10^(-26) xx 10^(24)`
`therefore k= 707.5 xx 10^(-2)`
`therefore k approx 7.1 N"/"m`.