Question

The volume of a cell in six dimensional phase space is -a-h^3,b-h^6,c-h^-3,d-
h^-6​

Answer 1

Answer:

Algebra is one of the broad areas of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.

Explanation:

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Answer 2

Answer:

The volume of a cell in six dimensional phase space is h³.

Therefore, the option (a) is correct.

Explanation:

Phase space is a hypothetical space where molecule as a point in the space.

• As we know any translational motion of a particle has six dimensions.

1. Three positional coordinates x, y and z
2. Three conjugate momenta coordinates, $P_x,\; P_y\; and\; P_z$

• Volume of the element can be dx, dy and dz.
• $P_x,\; P_y\; and\; P_z$ can be potted in three perpendicular distances and consider the volume dpx, dpy and dpz.
• Six dimensional space can be imagined in which dx, dy, dz, dpx, dpy and dpz are the element of volume.
• Element of volume in space is called cell.

Now divide the a phase into samll six dimensional cells with sides $dx, \;dy,\;dz,\; dp_x,\; dp_y,\;dp_z$

The volume of these cells, $d\tau=d x \;dy\;dz\; dp_x\; dp_ydp_z$

From Uncertainty principle:-

$dx\;dp_x\geq h$   and $dy\;dp_y\geq h$    and  $dz\;dp_z\geq h$

Therefore, $d\tau = h^3$

Therefore, a point in a phase space is considered to be a cell. The minimum volume of a cell in six dimensional phase space is of the order h³.

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