# Chapter 24 Atoms¶

## Example 24.1 Page no 1264¶

In [7]:
#Given
k=7.68*10**6*1.6*10**-19                   #J
e=1.6*10**-19
Z=29
m=9*10**9

#Calculation
r=(m*2*Z*e**2)/k

#Result
print"The distance of the closest approach is",round(r*10**14,1)*10**-14,"m"

The distance of the closest approach is 1.1e-14 m


## Example 24.2 Page no 1265¶

In [20]:
#Given
a=10                        #degree
e=1.6*10**-19
Z=79
m=9*10**9
a=5.0*1.6*10**-13

#Calculation
import math
b=(Z*e**2*(1/(math.tan(5*3.14/180.0)))*m)/a

#Result
print"Impact parameter is", round(b*10**13,1)*10**-13,"m"

Impact parameter is 2.6e-13 m


## Example 24.3 Page no 1265¶

In [25]:
#Given
Z=79
m=9*10**9
e=1.6*10**-19
r=4.0*10**-14

#Calculation
K=(m*2*Z*e**2)/(r*1.6*10**-13)

#Result
print"Energy is", round(K,2),"Mev"

Energy is 5.69 Mev


## Example 24.4 Page no 1265¶

In [31]:
#Given
v=2.1*10**7                        #m/s
a=4.8*10**7                        #C/Kg
Z=79
e=1.6*10**-19
m=9*10**9

#Calculation
r0=(2*m*Z*e*a)/v**2

#Result
print"Distance of the closest approach is", round(r0*10**14,1)*10**-14,"m"

Distance of the closest approach is 2.5e-14 m


## Example 24.6 Page no 1266¶

In [47]:
#Given
Z=79
e=1.6*10**-19                 #C
v=1.6*10**-12
m=9*10**9

#Calculation
import math
b=(m*Z*e**2*(1/(math.tan(45*3.14/180.0))))/v

#Result
print"(a) Scattering angle is 180 degree"
print"(b) The value of scattering angle decreases"
print"(c) Impact parameter is", round(b*10**14,1)*10**-14,"m"
print"(d) The scattering of particle takes place due to charge on the nucleus",
print"(e) Scattering angle is increase with decrease in impact parameter"

(a) Scattering angle is 180 degree
(b) The value of scattering angle decreases
(c) Impact parameter is 1.1e-14 m
(d) The scattering of particle takes place due to charge on the nucleus (e) Scattering angle is increase with decrease in impact parameter


## Example 24.7 Page no 1280¶

In [62]:
#Given
e=8.854*10**-12
h=6.62*10**-34
m=9*10**-31
e1=1.6*10**-19

#Calculation
import math
r1=((e*h**2)/(math.pi*m*e1**2))*10**10
v1=e1**2/(2*e*h)
n=2*r1

#Result
print"Radius of first orbit is", round(r1,2),"A"
print"Velocity of electron is",round(v1*10**-6,1),"*10**6 m/s"
print"Size of hydrogen atom is",round(n,2),"A"

Radius of first orbit is 0.54 A
Velocity of electron is 2.2 *10**6 m/s
Size of hydrogen atom is 1.07 A


## Example 24.8 Page no 1281¶

In [82]:
#Given
n=1.0
n1=2.0
n2=3.0
a=0.53*10**-10
Z=3.0

#Calculation
r1=(a*n)/Z
r2=(a*n1**2)/Z
r3=(a*n2**2)/Z
E1=(-13.6*Z**2)/n**2
E2=(-13.6*Z**2)/n1**2
E3=(-13.6*Z**2)/n2**2
E=E3-E1

#Result
print"(i) Radii of three lowest allowed orbits is", round(r1*10**10,2),"A,",round(r2*10**10,2),"A and",r3*10**10,"A"
print"(ii) Energy of three lowest allowed orbits is",E1,"ev,",E2,"ev and",E3,"ev"
print"Energy of the photon is",E,"ev"

(i) Radii of three lowest allowed orbits is 0.18 A, 0.71 A and 1.59 A
(ii) Energy of three lowest allowed orbits is -122.4 ev, -30.6 ev and -13.6 ev
Energy of the photon is 108.8 ev


## Example 24.9 Page no 1281¶

In [86]:
#Given
n=2.0
n1=3.0

#Calculation
E2=-13.6/n**2
E3=-13.6/n1**2

#Result
print"Energies of two energy level is",E2,"ev and",round(E3,2),"ev"

Energies of two energy level is -3.4 ev and -1.51 ev


## Example 24.10 Page no 1282¶

In [90]:
#Given
Rh=1.097*10**7

#Calculation
l=9/(8.0*Rh)

#Result
print"Wavelength of second line is",round(l*10**10,0),"A"

Wavelength of second line is 1026.0 A


## Example 24.11 Page no 1282¶

In [95]:
#Given
Rh=1.097*10**7

#Calculation
l=4/Rh

#Result
print"Shortest wavelength is",round(l*10**10,0),"A"

Shortest wavelength is 3646.0 A


## Example 24.12 Page no 1282¶

In [99]:
#Given
Rh=1.097*10**7

#Calculation
l=4/(3.0*Rh)

#Result
print"Longest wavelength is",round(l*10**10,0),"A"

Longest wavelength is 1215.0 A


## Example 24.13 Page no 1282¶

In [104]:
#Given
n=1.0
h=6.62*10**-34
c=3*10**8
f=1.6*10**-19
Z=2

#Calculation
E1=(-13.6*Z**2)/n**2
l=-(h*c)/(E1*f)

#Result
print"Minimum wavelength is", round(l*10**10,0),"A"

Minimum wavelength is 228.0 A


## Example 24.14 Page no 1283¶

In [112]:
#Given
n=1
Z=1.0
a=0.53*10**-10
Z1=4.0

#Calculation
import math
rh=(a*n)/Z**2
n1=math.sqrt((a*Z1/rh))
Eh=(-13.6*Z**2)/n**2
Ebe=(-13.6*Z1**2)/n1**2
E=Ebe/Eh

#Result
print"Energy of two states is",E

Energy of two states is 4.0


## Example 24.15 Page no 1283¶

In [116]:
#Given
Z=2
e=1.6*10**-19
e1=8.854*10**-12
n=3
h=6.62*10**-34
c=3*10**8

#Calculation
v=(Z*e**2)/(2*e1*n*h)
a=v/c

#Result
print"Speed of the electron is",round(a,3 )

Speed of the electron is 0.005


## Example 24.16 Page no 1284¶

In [118]:
#Given
r=10**-10
R=10**-15
Rs=7*10**8

#Calculation
R1=r/R
Re=R1*Rs

#Result
print"Radius of the earth's orbit is",Re,"m. Thus the earth would be much farther away from the sun"

Radius of the earth's orbit is 7e+13 m. Thus the earth would be much farther away from the sun


## Example 24.17 Page no 1284¶

In [131]:
#Given
E=-13.6*1.9*10**-19                #J
m=9*10**9
e=1.6*10**-19
n=1
c=3*10**8

#Calculation
r=(-e**2*m)/(2.0*E)
v=c/(137*n)

#Result
print"Velocity of the electron is",round(v*10**-6,1),"*10**6 m/s"

Orbital radius is 4.5e-11 m
Velocity of the electron is 2.2 *10**6 m/s


## Example 24.18 Page no 1284¶

In [135]:
#Given
v=2.2*10**6
r=5.3*10**-11

#Calculation
import math
f=v/(2*math.pi*r)

#Result
print"Initial frequency of light is",round(f*10**-15,1)*10**15,"Hz"

Initial frequency of light is 6.6e+15 Hz


## Example 24.19 Page no 1285¶

In [139]:
#Given
m=10                 #Kg
T=2*60*60             #S
rn=8*10**6            #m
h=6.62*10**-34

#Calculation
import math
vn=(2*math.pi*rn)/T
n=(2*math.pi*rn*vn)/h

#Result
print"Quantum number is",round(n*10**-44,1)*10**45

Quantum number is 5.3e+45


## Example 24.20 Page no 1285¶

In [148]:
#Given
E2=18.70
E1=16.70
h=6.62*10**-34
c=3*10**8

#Calculation
E=E2-E1
l=(h*c)/(E*1.6*10**-19)

#Result
print"Wavelength is", round(l*10**9,0),"nm"

Wavelength is 621.0 nm


## Example 24.21 Page no 1285¶

In [151]:
#Given
n1=2
n2=3
lb=6563
a=20
b=108.0

#Calculation
l1=(lb*a)/b

#Result
print"Wavelength of first member is",round(l1,0),"A"

Wavelength of first member is 1215.0 A


## Example 24.22 Page no 1285¶

In [158]:
#Given
Rh=1.097*10**7                         #/m
h=6.63*10**-34
c=3*10**8
n=2.0
n1=4.0

#Calculation
E=(h*c*Rh*(1/n**2-1/n1**2))/1.6*10**-19

#Result
print"Minimum energy is", round(E*10**38,2),"ev"

Minimum energy is 2.56 ev


## Example 24.23 Page no 1286¶

In [167]:
#Given
Rh=1.097*10**7
n2=4.0
n1=3.0

#Calculation
lm=1/(Rh*(1/n1**2-1/n2**2))
lm1=9/Rh

#Result
print"Wavelength is", round(lm1*10**9,1),"nm. This wavelength is in infrared part"

Wavelength is 820.4 nm. This wavelength is in infrared part