Question

The energy of the Principal energy state of Hydrogen and
Hydrogen like atoms is given by E = -2π^2 mk^2 z^2 e^4÷n²h²
a) what is the significance of the negative sign in the expression ?​

Answer 1

Answer:

Explanation:

Let the electron of mass m revolves around a nucleus (H-atom) in an orbit of radius r

n

​

with linear velocity v

n

​

.

As the electron revolves in an stationary orbit, thus centrifugal force acting on the electron is balanced by the coulombic force i.e. F

centrifugal

​

=F

coulomb

​

∴

r

n

​

mv

n

2

​

​

=

r

n

2

​

ke

2

​

where k=

4πϵ

o

​

1

​

=9×10

9

⟹ r

n

​

=

mv

n

2

​

ke

2

​

Also we use mv

n

​

r

n

​

=

2π

nh

​

Eliminating v

n

​

from both equations, we get r

n

​

=

m

ke

2

​

.

n

2

h

2

4π

2

m

2

r

n

2

​

​

⟹ r

n

​

=

4π

2

mke

2

h

2

n

2

​

Putting m=9.1×10

−31

kg, h=6.626×10

−34

Js and e=1.6×10

−19

C

We get radius of n

th

Bohr orbit r

n

​

=0.529 n

2

A

o