The speed of sound is given by the Newton-Laplace equation:
$$ v = \sqrt{\frac{K}{\rho}} $$
where $K$ is the bulk modulus (i.e. a measure of stiffness) and $\rho$ is the density. The physical interpretation of this is fairly obvious. Stiffer substances recoil faster from a displacement so incre...
Suppose you have a spring with a force constant $k$ and you compress it a distance $dx$ then the force is $F=kdx$. A stiffer spring has a higher $k$ so it produces a greater force for the same displacement.
If you have some mass attached to the spring then the greater force means a greater acceleration so the stiffer spring accelerates object attached to it faster.
I've just logged into work and we have all sorts of problems this morning. Probably due to storms we're having in the UK at the moment. I may be tied up for a bit sorting this out.
The binding energy of a nucleus, or indeed any bound state is negative, i.e. if you start with an isolated neutron and proton and bring them together then when they form a bound state they emit energy.
This means the mass of a bound state is less than the total mass of its components.
If you look at the masses given in the question you'll see that the mass of the deuteron is 1876MeV while if you add together the messages of the proton and neutron they come to 1879MeV. i.e. the deuteron is 3MeV lighter than it's components.
Well, suppose you want to split the deuteron back into a proton and neutron, that means you need to supply 3MeV of energy to do this. It's kind of like ionising an atom. If you want to split a hydrogen atom into a proton and electron you have to supply 13.6eV of energy.
The deuteron has to absorb a 3Mev photon to supply the energy needed to split it apart. Just like a hydrogen atom has to absorb a 13.6eV photon to ionise it.
But consider tritium. Thus is also a bound state, so the tritium nucleus weighs less than a proton and two neutrons. So it should be stable with respect to decay into a proton and three neutrons. Yes?
But tritium is unstable. It decays with a half life of about 12 years. So we have something weird here. Can you suggest why it is unstable even though it's a bound state?
Tritium is a bound state so when you form it from a proton and two neutrons that releases energy. So to make tritium decay back to a proton and two neutrons you would have to supply energy.
Yes. In tritium decay one of the neutrons converts to a proton and an electron. The electron is released as a beta particle, and the remaining two protons and neutron form a lower energy state than the single proton and two neutrons in tritium.
So as a whole the process releases energy. That energy is released as the energy of the electron.
The point of all this is that when we talk about a Q value we are always refering to a spontaneous decay like tritium to 3He and the Q value is the amount of energy released in this decay.
We wouldn't normally use the term Q value for the energy we have to supply to split up a nucleus. Q value always refers to energy released and it's always positive.
That's just terminology. I'm not sure what term is used to describe the energy we have to supply to split up a nucleus.
The Q value is the initial mass minus the final mass i.e. it's the amount of mass that got turned into energy. In this case we are told the Q value is 50MeV.
If you work in the COM frame the total momentum has to be zero, so the alpha particle goes one way and the nucleus goes the other.
From the info given you can calculate the momentum of the alpha particle, so the momentum of the daughter nucleus must be equal and opposite. You know the KE of the duaghter is 2MeV so you calculate its mass.
NB energy and momentum are linked by $p = \sqrt{2mE}$
@JohnRennie, A coil of wire wrapped on a hollow tube and a light bulb are connected in series to an ac source. What happens to the brightness of bulb when an iron rod is inserted in the tube?
@Zerix yes. It's easy to forget that both the emitted particle and the nucleus recoil after the decay. I must admit I forgot in this case, which is why I wasn't sure how to do it at first. I take it you got the answer (A)?
@blue_eyed_... yes, the inductance will increase. If you draw a phasor diagram it should be obvious that increasing the inductance is going to increase the overall impedance.
The question is asking: suppose we are watching one particular nucleus and we watch it for five half lives and it doesn't decay. Then for this particular nucleus what is the probabulity that it will decay in the next (sixth) half life?
The point is that just because a nucleus survives five half lives that doesn't make it special. Just by pure chance we expect $1/2^5$ nuclei will survive five half lives.
It's like if you flip a coin five times and it comes up heads every time. Then you flip it one more time what is the probability that it will come up heads again?
Two moles of ideal helium gas are in a rubber balloon at 30C. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to 35C. The amount of heat required in raising the temperature is nearly (take R=8.31 J/mol K)
@JohnRennie Also, a small conceptual doubt- What exactly is an instanteous axis of rotation? I always used it in problem solving as the point where perpendiculars drawn to the velocities of any two points of a rigid body meet, but this is obviously not the actual meaning of the thing
@JohnRennie Also, on a separate note, why does the need for the Coriolis force arise when we are analysing,say, a coin rotating about an axis while sitting on that coin? it seems to me that centrifugal force is good enough for a pseudo force?
@Abcd Yeah ik it is not in syllabus...But experts at my coaching are guessing that this and a few other topics in physics might be given as a new comprehension
@Abcd Yeah? Well...It is really amazing that I know about frontier MO theory...and then in the paper I forgot the basic integral dx/underoot((x^2+ a^2)) in tension
@Abcd I managed to bring my percentile just at the edge of the 99 percentile decimals inspite of my chemistry percentile...That's how "good" I am at the rest of the two..And I am not sharing the entire number...It just sucks
@Abcd Yeah, I also feel that this percentile system is biased....The marks I am getting...I should have had a much better rank with these marks in previous years...I was shocked at the number when it was converted
And the damn idiots never disclosed the actual marks
@AvnishKabaj I mean...I know the technicalities...I have seen the details countless times..But then, all the 10 toppers from my coaching(who are expecting ranks in 3k in advanced) were present on 9th and 10th, probably because they registered early, idk. So, it obviously affected my percentile, and I still don't know my marks exactly for my own satisfaction
And many toppers from various institutes were there on 9th and 10th...Fiitjee, Akash,VMC etc. I feel that the student pool wasn't that well mixed, although I don't claim any =thing
@Abcd They can randomly shuffle roll numbers in between slots...All the roll numbers were given serialwise as per registration...And they were sent in the same order... Otherwise Iw ouldn't have seen all these magical guys on my shift all together
The speed of sound is given by the Newton-Laplace equation:
$$ v = \sqrt{\frac{K}{\rho}} $$
where $K$ is the bulk modulus (i.e. a measure of stiffness) and $\rho$ is the density. The physical interpretation of this is fairly obvious. Stiffer substances recoil faster from a displacement so incre...
Problem Solving Strategies
Problem Solving Strategies