August 22, 2013

Explain whether atomic number can increase during nuclear decay .Support your answer with example.

Ans.When a beta particle is emitted out of any nucleus,then it's mass number does not undergo any change but it's charge number increase by one.Negative Beta is an electron and its emission from the nucleus becomes an in comprehensive enigma, as there is no electron in the nucleus >how ever , the emission of electrom from the nucleus can be thought of as neutron emitting an electron and becoming a proton, although the modern explanation is not that simple.
This means that beta particle is formed at the time of emission.That is why at the time of emission of a beta particle the charge number of nucleus increases by one.

For Example:

August 11, 2013

what is a directional derivative/gradient?

Directional Derivative

The directional derivative del _(u)f(x_0,y_0,z_0) is the rate at which the function f(x,y,z) changes at a point (x_0,y_0,z_0)in the direction u. It is a vector form of the usual derivative, and can be defined as
del _(u)f=del f·(u)/(|u|)
(1)
=lim_(h->0)(f(x+hu^^)-f(x))/h,
(2)
where del  is called "nabla" or "del" and u^^ denotes a unit vector.
The directional derivative is also often written in the notation
d/(ds)=s^^·del
(3)
=s_xpartial/(partialx)+s_ypartial/(partialy)+s_zpartial/(partialz),
(4)
where s denotes a unit vector in any given direction and partialf/partialx=f_x denotes a partial derivative.
Let u^^=(u_x,u_y,u_z) be a unit vector in Cartesian coordinates, so
 |u^^|=sqrt(u_x^2+u_y^2+u_z^2)=1,
(5)
then


 del _(u^^)f=(partialf)/(partialx)u_x+(partialf)/(partialy)u_y+(partialf)/(partialz)u_z.
(6)