Solve MUONs Numerical Problem with Help from Experts - Free Consultation

[shaiqbashir]

MUONs problem---pl\ help

Hi Guys!

well! i came across a terrible type of problem which includes particles named MUONS. please help me in solving this numerical:
It goes like this:

"MUONs are the particles having masss about 207 times that of electron. they are present in the cosmic rays. Muons are captured by atoms and orbit like electrons. However muons will orbit much closer to the nucleus than any electron.

a) calculate the radius of a muon in orbit when captured by a uranium atom
b)how much energy would be liberated if the muon was initially at the rest before being captured?
c)the radius of the uranium nucleus is 7.5fm. how does your answer in (a) compare with this number?

ur early reply shall be highly appreciated!

thanks in advance!

 

[arivero]

shaiqbashir, first, the context of the problem, is it classical or quantum mechanical? Probably iy is QM, and you are fortunate the muon is different particle from the electron, so you do not need to think about Pauli principle etc.

All you are being asked, it seems. is to use the hidrogen atom solution but using a mass 207 times the electron and 235 times the nucleus. Thus the effective mass is $${207 * 235 * m_e * m_n } \over 207 m_e + 235 m_n}$$. Had the teacher been a bit more generous, s/he had asked you to calculate the capture inside a Pb atom instead of U. The emphasis in U is surely to try to get conclusions about muon induced nuclear effects.

The only thing I am not sure is if your teacher expects you to use Z=92 or Z=1 or some effective charge taking into account the extant electrons. As a minimum, you can first to give an answer depending of Z.

 

[WhiteWolf]

wow, this may be a little elementary considering what I just read here, but I also have a question about muons. Ummm, my dumb teacher didnt know how to answer this, so I came here, when cosmic rays hit the Earth's atmosphere, they and converted from energy into particles know as muons. Now I noticed that the Law of Conservation of Charge states that a charge cannot be created, just transferred. But when the muons are created, they carry a negative charge. My teacher said energy in itself cannot carry a charge, so what gives with muons? Is the surrounding air made positive or something?

(Also I heard that these muons are traveling at light speeds, and even though they have extremely short halflives, they hit our bodies almost instantly, and are responsible for mutations in DNA, is this also true?)

 

[Astronuc]

. . . when cosmic rays hit the Earth's atmosphere, they and converted from energy into particles know as muons. Now I noticed that the Law of Conservation of Charge states that a charge cannot be created, just transferred. But when the muons are created, they carry a negative charge. My teacher said energy in itself cannot carry a charge, so what gives with muons? Is the surrounding air made positive or something?

(Also I heard that these muons are traveling at light speeds, and even though they have extremely short halflives, they hit our bodies almost instantly, and are responsible for mutations in DNA, is this also true?)

On earth, a muon is created when a charged pion decays. The pions are created in an upper atmosphere by cosmic radiation and have a very short decay time--a few nanoseconds. The muons created when the pion decays are also short-lived: their decay time is 2.2 microseconds. However, muons in the atmosphere are moving at very high velocities, so that the time dilation effect of special relativity make them easily detectable at the Earth's surface.

from http://en.wikipedia.org/wiki/Muon

A positive pion will decay into a positive muon, but it is the negative muon that is of interest with respect to muonic atoms.

The rate of muon interactions at the Earth's surface is very low - essentially less than 1 event/sec (i.e. background) - I have first hand experience with this. Considering that muons have always been part of the environment, there is no need to worry about their effects on human tissue.

 

[WhiteWolf]

But wouldn't a positive muon be antimatter? Even if my physics book is wrong, the dictionary defines muons as negatively charged. Unless you don't believe in evolution... what does cause genetic mutations? You don't have exact 50% copies of your parents DNA.

 

[Astronuc]

But wouldn't a positive muon be antimatter? Even if my physics book is wrong, the dictionary defines muons as negatively charged. Unless you don't believe in evolution... what does cause genetic mutations? You don't have exact 50% copies of your parents DNA.

The positive muon is the anti-particle of the negative muon, and vice-versa.

Muons come from decay of pions.

$\pi^+ \rightarrow \mu^+ + \nu_\mu$
$\pi^- \rightarrow \mu^- + \bar{\nu}_\mu$

and muons decay to electrons by

$\mu^+ \rightarrow e^+ + \nu_\mu + \bar{\nu}_e$
$\mu^- \rightarrow e^- + \nu_\mu + \bar{\nu}_e$

charged particle interact with matter by colliding with electrons, knocking them out of the atoms (ionziation) and consequently disrupting bonds.

The positron e⁺ combines with an electron and they annhiliate with the production of two gamma rays.

Pions originate in the decay of baryonic resonances, which are produced by antimatter-matter reactions (p + $\bar{p}$) or when pion or Kaons interact with protons (or neutrons) in the Earth's upper atmosphere.

Mutations, or disruption of the DNA replication process, may be caused by a number of agents, including radiation, of which muons are one type. At the Earth's surface, muons are relatively rare compared to natural radiation in the body or other environmental sources. Also, there are bio-agents (viruses which impart their DNA into host cells) and chemicals which can affect human or animal DNA or other cell processes. Then there are factors like malnutrition, improper diet, or smoking of tobacco.