In [1]:

    

import numpy as np


    

In [ ]:

    

def mean_life(half_life):
    return half_life / np.log(2)


    

In [10]:

    

def remaining(time, initial=1.0, half_life=1, t0=0):
    
    return initial * np.exp(-1 * (time - t0)/(mean_lifetime))


    

In [11]:

    

def problem_8_8_E():
    U238_halflife = 4.51e9 #years
    Th234_halflife = 21.4 / 365.25 #days / (days/years)
    Ph234_halflife = 6.75 / 24.0 / 356.25 # hours / (hours/day) / (days/year)
    
    initial_U234 = 1.0
    
    U234_halflife = 2.47e5 #years
    l_earth = 4.54e9 #years
    
    return remaining(time=l_earth, initial=1.0, half_life=U234_halflife)


    

In [29]:

    

print problem_8_8_E()


    

    




0.0

In [30]:

    

np.exp(-1000)


    

    
Out[30]:





0.0

In [ ]:

    

t = 4.5e9
lambda_1 = np.log(2) / 4.51e9
lambda_2 = np.log(2) / 2.47e5


    

In [33]:

    

N_0 = .0093 / np.exp(-lambda_1 * t)
print N_0


    

    




0.0185714353985

In [34]:

    

print ((N_0 * lambda_1) / (lambda_2 - lambda_1)) * (np.exp(-lambda_1 * t) - np.exp(-lambda_2 * t))


    

    




5.09362707891e-07

In [34]:

    




    

In [34]:

    




    

In [35]:

    

np.exp(5.0 / 25) / np.exp(5 / 35.)


    

    
Out[35]:





1.0588070577429671

In [36]:

    

np.exp(5/25.- 5/35.)


    

    
Out[36]:





1.0588070577429671

In [37]:

    

import matplotlib.pyplot as plt


    

In [38]:

    

plt.ion()


    

In [39]:

    

plt.plot(np.exp(np.linspace(0,100,100) * 1/(-.00001)))


    

    
Out[39]:





[<matplotlib.lines.Line2D at 0x117c6ec90>]

In [40]:

    

plt.show()


    

In [41]:

    

print 5


    

    




5

In [42]:

    

def n_initial(n_now, t, t_m):
    return n_now / (np.exp(-(t)/t_m))


    

In [46]:

    

print'U235 initial:', n_initial(6.49e-5, 4.5e9, 7.1e8 / np.log(2))


    

    




U235 initial: 0.0052502657816

In [45]:

    

print 'U238 initial:', n_initial(8.49e-3, 4.5e9, 4.5e9 / np.log(2))


    

    




U238 initial: 0.01698

In [51]:

    

def n_daughter_initial(n_now, np_initial, t, t_m):
    return n_now - np_initial * (1-np.exp(-t/t_m))


    

In [52]:

    

print 'Pb206 initial:', n_daughter_initial(.603, .01698, 4.5e9, 4.5e9 / np.log(2))


    

    




Pb206 initial: 0.59451

In [53]:

    

print 'Pb207 initial:', n_daughter_initial(.650, .00525, 4.5e9, 7.1e8 / np.log(2))


    

    




Pb207 initial: 0.644814896715

In [54]:

    

.6448 / .0612


    

    
Out[54]:





10.535947712418302

In [65]:

    

.1224 * 10.54


    

    
Out[65]:





1.290096

In [62]:

    




    

In [66]:

    

.59451 / .0613


    

    
Out[66]:





9.69836867862969

In [68]:

    

.1224 * 9.698


    

    
Out[68]:





1.1870352

In [63]:

    

(7.1e8 / np.log(2)) * np.log(((2.63 - 1.29) / 1.59e-2) + 1)


    

    
Out[63]:





4553996945.817317

In [64]:

    

'%3.2e' % (4553996945.817317)


    

    
Out[64]:





'4.55e+09'

In [70]:

    

(2.63 - 1.29) / (1-np.exp(-4.55e9/ (7.1e8/np.log(2)) ) )


    

    
Out[70]:





1.3559629047017809

In [72]:

    

.00525 / .01698


    

    
Out[72]:





0.3091872791519435

In [73]:

    

1.355 * .309


    

    
Out[73]:





0.418695

In [75]:

    

.419* np.exp(-4.55e9 / (4.5e9/np.log(2)))


    

    
Out[75]:





0.20789270474208665

In [76]:

    

1.187 + .417 * (1 - np.exp(-4.55e9 /  (4.5e9/np.log(2)) ) )


    

    
Out[76]:





1.3970996232041764

In [ ]: