Radioactive decay is given by:
N = No x e^(-λt)
We know that N/No has to be 0.05
λ = 0.15
0.05 = e^(-0.15t)
t = ln(0.05)/(-0.15)
t = 19.97 days
Answer:
![E=3.5(8.98*10^{6}x-2.69*10^{15}t)](https://tex.z-dn.net/?f=E%3D3.5%288.98%2A10%5E%7B6%7Dx-2.69%2A10%5E%7B15%7Dt%29)
Explanation:
The electric field equation of a electromagnetic wave is given by:
(1)
- E(max) is the maximun value of E, it means the amplitude of the wave.
- k is the wave number
- ω is the angular frequency
We know that the wave length is λ = 700 nm and the peak electric field magnitude of 3.5 V/m, this value is correspond a E(max).
By definition:
And the relation between λ and f is:
![c=\lambda f](https://tex.z-dn.net/?f=c%3D%5Clambda%20f)
![f=\frac{c}{\lambda}](https://tex.z-dn.net/?f=f%3D%5Cfrac%7Bc%7D%7B%5Clambda%7D)
![f=\frac{3*10^{8}}{700*10^{-9}}](https://tex.z-dn.net/?f=f%3D%5Cfrac%7B3%2A10%5E%7B8%7D%7D%7B700%2A10%5E%7B-9%7D%7D)
![f=4.28*10^{14}](https://tex.z-dn.net/?f=f%3D4.28%2A10%5E%7B14%7D)
The angular frequency equation is:
![\omega=2\pi f](https://tex.z-dn.net/?f=%5Comega%3D2%5Cpi%20f)
![\omega=2\pi*4.28*10^{14}](https://tex.z-dn.net/?f=%5Comega%3D2%5Cpi%2A4.28%2A10%5E%7B14%7D)
![\omega=2.69*10^{15} [rad/s]](https://tex.z-dn.net/?f=%5Comega%3D2.69%2A10%5E%7B15%7D%20%5Brad%2Fs%5D)
Therefore, the E equation, suing (1), will be:
(2)
For the magnetic field we have the next equation:
(3)
It is the same as E. Here we just need to find B(max).
We can use this equation:
![E_{max}=cB_{max}](https://tex.z-dn.net/?f=E_%7Bmax%7D%3DcB_%7Bmax%7D)
![B_{max}=\frac{E_{max}}{c}=\frac{3.5}{3*10^{8}}](https://tex.z-dn.net/?f=B_%7Bmax%7D%3D%5Cfrac%7BE_%7Bmax%7D%7D%7Bc%7D%3D%5Cfrac%7B3.5%7D%7B3%2A10%5E%7B8%7D%7D)
![B_{max}=1.17*10^{-8}T](https://tex.z-dn.net/?f=B_%7Bmax%7D%3D1.17%2A10%5E%7B-8%7DT)
Putting this in (3), finally we will have:
(4)
I hope it helps you!
i'm stuck on that question also
Answer:
The true weight of the aluminium is
4.5021 kg
Explanation:
Given data
= 4.5 kg
= 1.29 ![\frac{kg}{m^{3} }](https://tex.z-dn.net/?f=%5Cfrac%7Bkg%7D%7Bm%5E%7B3%7D%20%7D)
= 2.7× ![10^{3} \frac{kg}{m^{3} }](https://tex.z-dn.net/?f=10%5E%7B3%7D%20%5Cfrac%7Bkg%7D%7Bm%5E%7B3%7D%20%7D)
The true mass of the aluminium is given by
![m_{alu} = \frac{\rho_{alu}m_{app}}{\rho_{alu} -\rho_{air} }](https://tex.z-dn.net/?f=m_%7Balu%7D%20%3D%20%5Cfrac%7B%5Crho_%7Balu%7Dm_%7Bapp%7D%7D%7B%5Crho_%7Balu%7D%20-%5Crho_%7Bair%7D%20%7D)
Put all the values in above equation we get
![m_{alu} = \frac{(2700)(4.5)}{2700-1.29}](https://tex.z-dn.net/?f=m_%7Balu%7D%20%3D%20%5Cfrac%7B%282700%29%284.5%29%7D%7B2700-1.29%7D)
4.5021 kg
Therefore the true weight of the aluminium is
4.5021 kg
Solution
distance travelled by Chris
\Delta t=\frac{1}{3600}hr.
X_{c}= [(\frac{21+0}{2})+(\frac{33+21}{2})+(\frac{55+47}{2})+(\frac{63+55}{2})+(\frac{70+63}{2})+(\frac{76+70}{2})+(\frac{82+76}{2})+(\frac{87+82}{2})+(\frac{91+87}{2})]\times\frac{1}{3600}
=\frac{579.5}{3600}=0.161miles
Kelly,
\Delta t=\frac{1}{3600}hr.
X_{k}=[(\frac{24+0}{2})+(\frac{3+24}{2})+(\frac{55+39}{2})+(\frac{62+55}{2})+(\frac{71+62}{2})+(\frac{79+71}{2})+(\frac{85+79}{2})+(\frac{85+92}{2})+(\frac{99+92}{2})+(\frac{103+99}{2})]\times\frac{1}{3600}
=\frac{657.5}{3600}
\Delta X=X_{k}-X_{C}=0.021miles