# Chapter02: Structure of atoms¶

## Ex2.1:pg-12¶

In [2]:
#Example 2.1 : radius of the first bohr"s orbit

#given data :

ep=8.854*10**-12;#
h=6.626*10**-34;#
m=9.1*10**-31;#in Kg
e=1.602*10**-19;#
r1=((ep*(h**2))/((math.pi*m*(e**2))));#

0.53 is radius,r1(in angstrom)


## Ex2.2:pg-12¶

In [4]:
#Example 2.2 : radius of the second bohr"s orbit

#given data :

r1_h=0.529; # radius for hydrozen atom in Angstrum
n1=1;# for the first bohr's orbit of electron in hydrozen atom
Z1=1; # for the first bohr's orbit of electron in hydrozen atom
k=(r1_h*Z1)/n1**2; # where k is constant
n2=2; # for the second bohr orbit
Z2=2; #for the second bohr orbit
r2_he=k*(n2**2/Z2);
print r2_he," is radius of the second bohr orbit,r2 in (Angstrom) "

1.058  is radius of the second bohr orbit,r2 in (Angstrom)


## Ex2.3:pg-13¶

In [1]:
# Example 2.3: to prove

Z=1;#assume
n1=1;#orbit 1
n2=2;#orbit 2
n3=3;#orbit 3
e1=((-13.6*Z)/(n1**2));#energy for the first orbit
e2=((-13.6*Z)/(n2**2));#energy for the second orbit
e3=((-13.6*Z)/(n3**2));#energy for the third orbit
e31=e3-e1;#energy emitted by an electron jumping from orbit nuber 3 to orbit nimber 1
e21=e2-e1;#energy emitted by an electron jumping from orbit nuber 2 to orbit nimber 1
re=e31/e21;#ratio of energy
print round(re,2)," is equal to ratio of energy for an electron to jump from orbit 3 to orbit 1 and from orbit 2 to orbit 1 is 32/27 \n hence proved"

1.19  is equal to ratio of energy for an electron to jump from orbit 3 to orbit 1 and from orbit 2 to orbit 1 is 32/27
hence proved


## Ex2.4:pg-13¶

In [8]:
#Example 2.4 : velocity

import decimal

#given data :

h=6.626*10**-34;
e=1.6*10**-19;
epsilon_o=8.825*10**-12;
n=1;
Z=1;
vn=(Z*e**2)/(2*epsilon_o*n*h);
print "{:.3e}".format(vn)," is velocity,vn in (m/s) "

2.189e+06  is velocity,vn in (m/s)


## Ex2.5:pg-14¶

In [9]:
#Example 2.5 : velocity

#given data :
n=1;
Z=1;
k=6.56*10**15; # k is constant
fn=k*(Z**2/n**3);
print fn," is orbital frequency,fn in (Hz) "

6.56e+15  is orbital frequency,fn in (Hz)


## Ex2.6.a:pg-14¶

In [9]:
#Example 2.6.a : the energy of the photon emitted

#given data :
Z=1;#for hydrogen
n1=3;
n2=2;
E3=-(13.6*Z**2)/n1**2;
E2=-(13.6*Z**2)/n2**2;
del_E=E3-E2;
print round(del_E,2)," is the energy of photon emitted, del_E in (eV) "

1.89  is the energy of photon emitted, del_E in (eV)


## Ex2.6.b:pg-14¶

In [11]:
#Example 2.6.b : frequency

#given data :

Z=1;#for hydrozen
n1=3;
n2=2;
m=6.626*10**-34;# mass of electron in kg
E3=-(13.6*Z**2)/n1**2;
E2=-(13.6*Z**2)/n2**2;
del_E=E3-E2;
E=del_E*1.6*10**-19;# in joules
v=(E/m);
print round(v,-12),"frequency of the photon emitted,v(Hz) "

4.56e+14 frequency of the photon emitted,v(Hz)


## Ex2.6.c:pg-15¶

In [4]:
#Example 2.6.c : wave length of the photon emitted

#given data :

Z=1;#for hydrozen
n1=3;
n2=2;
m=6.626*10**-34;# mass of electron in kg
C=3*10**8;
E3=-(13.6*Z**2)/n1**2;
E2=-(13.6*Z**2)/n2**2;
del_E=E3-E2;
E=del_E*1.6*10**-19;
v=E/m;
lamda=C/v;
print round(lamda,9)," is wavelength of the photon emitted,(m) "

6.58e-07  is wavelength of the photon emitted,(m)