Why is electron energy negative in Bohr orbits?

[alijan kk]

Energy of electron in nth Bohr orbit.

En= -13.6 ev
n²

what does this negative sign mean here ? and why the electron has less energy as we increase n ,, explain me with the help of electric fields and coulumbs law. :

 

[Ygggdrasil]

By convention, the potential energy of a free, unbound electron is defined as zero. As the electron approaches a hydrogen nucleus, does it's potential energy go up or down?

 

[alijan kk]

By convention, the potential energy of a free, unbound electron is defined as zero. As the electron approaches a hydrogen nucleus, does it's potential energy go up or down?

i don,t i am right or wrong but i compare it with gravitational field,,, and as an electron goes near to the nucleus its potential energy decreases,

 

[Ygggdrasil]

That is correct. The electron feels an Coulombic attraction to the proton just as an object feels a gravitational attraction to the Earth. Movement of an object along the direction of this attraction decreases its potential energy (mathematically, you can express this by saying that change in potential energy of an object is the integral of the forces felt by that object as it moves along a certain path: http://hyperphysics.phy-astr.gsu.edu/hbase/pegrav.html).

 

[alijan kk]

That is correct. The electron feels an Coulombic attraction to the proton just as an object feels a gravitational attraction to the Earth. Movement of an object along the direction of this attraction decreases its potential energy (mathematically, you can express this by saying that change in potential energy of an object is the integral of the forces felt by that object as it moves along a certain path: http://hyperphysics.phy-astr.gsu.edu/hbase/pegrav.html).

so this negative sign means here decrease in potential energy of an electron ?

 

[Ygggdrasil]

If the potential energy starts at zero and decreases as the electron moves toward the nucleus, then the potential energy of an electron bound by the nucleus must be zero.

(in other words, the fact that E < 0 means that a bound electron has a lower potential energy that a free electron)

 

[drvrm]

what does this negative sign mean here ? and why the electron has less energy as we increase n ,, explain me with the help of electric fields and coulumbs law. :

the negative sign indicates that the electron is bound to the nucleus.
all binding energies are negative.

what is the potential energy of the electron in the field of nucleus ...write coulombs law and calculate the work done in bringing an electron to the radial distance say r.

So m.v^2 /r = centrepetal force = - K. Ze. e/ r^2 (coulomb attraction)

minus sign indicates that its directed towards center

so ( !/2)m.v^2 = 1/2 of mod {(-K. Ze. e)/ .r} but the expression in parenthesis is nothing bur Potential energy of the electron.

as the field is attractive it will do the work rather than the external agent...and that work will be reduction in PE ..a negative value less than zero. The zero of the potential lies at infinity.

So all energy levels of the Bohr model shells will be below Zero of total energy. E= T+V,
you can ask- the T= K.E. of electron is +ve so , total Energy can/may be positive..
.but you saw the Value of K.E. in an orbit and it comes to half of the V the PE in numbers so
total energy is negative half of the potential energy.

a common example of bound state is moon rotating around earth...the total energy is negative.
A zero energy means static free particle...and positive energy means free particle with velocity..

 

[alijan kk]

the negative sign indicates that the electron is bound to the nucleus.
all binding energies are negative.

what is the potential energy of the electron in the field of nucleus ...write coulombs law and calculate the work done in bringing an electron to the radial distance say r.

So m.v^2 /r = centrepetal force = - K. Ze. e/ r^2 (coulomb attraction)

minus sign indicates that its directed towards center

so ( !/2)m.v^2 = 1/2 of mod {(-K. Ze. e)/ .r} but the expression in parenthesis is nothing bur Potential energy of the electron.

as the field is attractive it will do the work rather than the external agent...and that work will be reduction in PE ..a negative value less than zero. The zero of the potential lies at infinity.

So all energy levels of the Bohr model shells will be below Zero of total energy. E= T+V,
you can ask- the T= K.E. of electron is +ve so , total Energy can/may be positive..
.but you saw the Value of K.E. in an orbit and it comes to half of the V the PE in numbers so
total energy is negative half of the potential energy.

a common example of bound state is moon rotating around earth...the total energy is negative.
A zero energy means static free particle...and positive energy means free particle with velocity..

i practiced to derive the potential energy expression,

"electron is bound more weakly bound when n is bigger"

if the electron has high potential energy if it is farther from nucleus (not at infinity) , then how it is loosely bound ? thankyou for your feedback

 

[drvrm]

if the electron has high potential energy if it is farther from nucleus (not at infinity) , then how it is loosely bound ?

If the electron is in a shell far from the Ze -nucleus then its radius is larger

the potential v is proportional to 1/r so r large means less negative potential
and r small means more negative potential

so the inner shell electron have higher binding energy than the outer shell
and a valence electron is almost close to V=0 so that it can travel around the material

So think about Total energy below zero line
-13,6 is lower than say -5.6 but bot are lower than zero.

just like a deep well and one is raising a bucket of water...so if the water is deeper more
negative energy more work to be done to take out the water and

if water level is shallow less amount of work necessary to bring it up to zero.