The nucleus of a certain atom has a radius of 4.0 ×10 – 15 m. An electron orbits

Question

The nucleus of a certain atom has a radius of 4.0 ×10–15 m. An electron orbits the nucleusat a radius of 1.5 × 10–10 m.Imagine the electron orbit is on the surface of a sphere and thatthe shape of the nucleus is spherical. Approximately how manynuclei would fit into the sphere on which the electronorbits?

a. 4.9 ×1011
b. 5.3 ×1013
c. 7.5 ×107
d. 3.8 ×104
e. 1.4 × 109 The nucleus of a certain atom has a radius of 4.0 ×10–15 m. An electron orbits the nucleusat a radius of 1.5 × 10–10 m.Imagine the electron orbit is on the surface of a sphere and thatthe shape of the nucleus is spherical. Approximately how manynuclei would fit into the sphere on which the electronorbits? 4.9 ×1011 5.3 ×1013 7.5 ×107 3.8 ×104 1.4 × 109

Explanation / Answer

The nucleus of a certain atom has a radius of 4.0 ×10–15 m. An electron orbits the nucleusat a radius of 1.5 × 10–10 m.Imagine the electron orbit is on the surface of a sphere and thatthe shape of the nucleus is spherical. Approximately how manynuclei would fit into the sphere on which the electron orbits?

volume of sphere orbitted by electron

V = 4*pi/3 *(1.5e-10)^3 = 4*pi/3 *r^3

Vof nucleus

V_nucl = 4*pi/3 *(4e-15)^3

Number nucl that can fit in V of sphere orbitted by electron:

V/V_nucl = 4*pi/3 *(1.5e-10)^3 /(4*pi/3*(4e-15)^3) =(1.5e-10/4e-15)^3 = 5.27 e13, PIck B

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