" The perpendicular distance of the initial velocity vector of the "alpha" - particle form the centre of nucleus is called "

An alpha -particle and a proton are fired through the same magnetic field which is perpendicular to their velocity vectors. The alpha -partcles and the proton move such that radius of curvature of their paths is same. Find the ratio of their de Broglie wavelengths.

Perpendicular distance of a point from line in vector and cartesian form

The ratio of de - Broglie wavelength of alpha - particle to that of a proton being subjected to the same magnetic field so that the radii of their path are equal to each other assuming the field induction vector vec(B) is perpendicular to the velocity vectors of the alpha - particle and the proton is

A free ^238U nucleus kept in a train emits an alpha particle. When the train is stationary, a nucleus decays and a passenger measures that the separation between the alpha particle and the recoiling nucleus becomes x at time t after the decay. If the decay takes place while the train is moving at a uniform velocity v, the distance betwen the alpha particle and the recoiling nucleus at a time t after the decay as measured by the passenger is

A nucleus moving with velocity bar(v) emits an alpha -particle. Let the velocities of the alpha -particle and the remaining nucleus be bar(v)_(1) and bar(v)_(2) and their masses be m_(1) and (m_2) then,

An (alpha) -particle and a proton are both simultaneously projected in opposite direction into a region of constant magnetic field perpendicular to the direction of the field. After some time it is found that the velocity of the (alpha) -particle has changed in a direction by 45^(@) . Then at this time, the angle between velocity vectors of (alpha) -particle and proton is