1)A molecule of DNA (deoxyribonucleic acid) is 2.29 µm long. The ends of the mol

Question

1)A molecule of DNA (deoxyribonucleic acid) is 2.29 µm long. The ends of the molecule become singly ionized: negative on one end, positive on the other. The helical molecule acts like a spring and compresses 1.20% upon becoming charged. Determine the effective spring constant of the molecule.
................. N/m

(b) State how the magnitude of this force compares with the magnitude of the gravitational force exerted by one proton on the other.

=  

(c) What must be a particle's charge-to-mass ratio if the magnitude of the gravitational force between two of these particles is equal to the magnitude of electric force between them?
C/kg

Explanation / Answer

Here ,

length of molecules , L= 2.29 um

change in length = 1.2 %

Now, let the effective spring constant is k

force = k * x

k * e^2/d^2 = K * x

9*10^9 * (1.602 *10^-19)^2 /(0.988 * 2.29 *10^-6)^2 = k * 0.012 * 2.29 *10^-6

solving for k

k = 1.642 *10^-9 N/m

the spring constant is 1.642 *10^-9 N/m

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