Question

Consider a simple model of the hydrogen atom where 1 electron is in a stable orbit around 1 proton at a distance of 0.05 nm. If the electron were moved to a larger stable orbit (say 0.1 nm), what would be the sign of: deltaU = the change in potential energy? deltaK = the change in kinetic energy? deltaE = the change in mechanical (potential plus kinetic) energy? Would moving the electron to a higher orbit require positive or negative work from external forces?

Answer 1

Potential energy of the electron at a distance r from the proton = U=
for hydrogen Z=1.

given that electron jumps from orbit 1 to higher orbit..

from the equation of the potential energy of the electron , when an electron jumps from lower to higher ,the potential energy of an electron increases as delta U = final potentail enery - initial kinetic energy

=- (which is positive) because (R>r)

where R is radius of higher orbit.

.so potentail energy increases as electron jumps from lower orbit to higher orbit...

=> SIGN OF CHANGE IN POTENTIAL ENERGY IS POSITIVE

Kinetic energy :

Kinetic energy of electron K =

for hydrogen Z=1,

change in kinetic energy = final kinetic energy - initial kinetic energy =e^2/(2R)-e^2/(2r)<0 because (R>r)

so the kinetic energy of an electron dreases when an electron moves from lower to higher orbit ..

=> SIGN OF CHANGE IN KINETIC ENERGY IS NEGATIVE