Answer:
The number of molecules in the volume is
molecules
Explanation:
From the question we are told that
The pressure of the ultrahigh vacuum is ![P = 8.4*10^{-11} torr = 8.4*10^{-11} * 133 = 1.1172 *10^{-8}Pa](https://tex.z-dn.net/?f=P%20%3D%208.4%2A10%5E%7B-11%7D%20torr%20%3D%20%208.4%2A10%5E%7B-11%7D%20%2A%20133%20%3D%201.1172%20%2A10%5E%7B-8%7DPa)
The molecular diameter of the gas molecules ![d = 2.2*10^{-10} m](https://tex.z-dn.net/?f=d%20%3D%20%202.2%2A10%5E%7B-10%7D%20m)
The temperature is ![T = 310 \ K](https://tex.z-dn.net/?f=T%20%3D%20%20310%20%5C%20K)
Avogadro's number is ![N = 6.02214 *10^{23}\ l/mol](https://tex.z-dn.net/?f=N%20%3D%20%206.02214%20%2A10%5E%7B23%7D%5C%20%20l%2Fmol)
The volume of the gas is ![V = 0.87 m^3](https://tex.z-dn.net/?f=V%20%3D%20%200.87%20m%5E3)
From the ideal gas law[
] that the number of mole is mathematically represented as
![n = \frac{PV}{RT}](https://tex.z-dn.net/?f=n%20%3D%20%5Cfrac%7BPV%7D%7BRT%7D)
Where R is the gas constant with a value ![R = 8.314\ J/mol](https://tex.z-dn.net/?f=R%20%3D%20%208.314%5C%20J%2Fmol)
Substituting values
![n = \frac{1.1172 *10^{-8} * 0.87}{8.314 * 310}](https://tex.z-dn.net/?f=n%20%3D%20%20%5Cfrac%7B1.1172%20%2A10%5E%7B-8%7D%20%2A%200.87%7D%7B8.314%20%2A%20310%7D)
![n = 3.771*10^{-12} \ mole](https://tex.z-dn.net/?f=n%20%3D%203.771%2A10%5E%7B-12%7D%20%20%5C%20mole)
The number of molecules is mathematically represented as
![N_v = n * N](https://tex.z-dn.net/?f=N_v%20%3D%20%20n%20%2A%20N)
Substituting values
![N_v = 3.771*10^{-12} * 6.02214 *10^{23}](https://tex.z-dn.net/?f=N_v%20%3D%20%203.771%2A10%5E%7B-12%7D%20%20%20%2A%206.02214%20%2A10%5E%7B23%7D)
molecules
Answer:
It would be A or a speed skater moving at an increasing speed on a straight track
Explanation:
the reasoning behind this is that the speed skater is getting faster or is accelerating.
Answer:
(a)
, (b)
, (c) ![W = -51](https://tex.z-dn.net/?f=W%20%3D%20-51)
Explanation:
The statement is incomplete:
The force on an object is
. For the vector
. Find: (a) The component of
parallel to
, (b) The component of
perpendicular to
, and (c) The work
, done by force
through displacement
.
(a) The component of
parallel to
is determined by the following expression:
![\vec F_{\parallel} = (\vec F \bullet \hat {v} )\cdot \hat{v}](https://tex.z-dn.net/?f=%5Cvec%20F_%7B%5Cparallel%7D%20%3D%20%28%5Cvec%20F%20%5Cbullet%20%5Chat%20%7Bv%7D%20%29%5Ccdot%20%5Chat%7Bv%7D)
Where
is the unit vector of
, which is determined by the following expression:
![\hat{v} = \frac{\vec v}{\|\vec v \|}](https://tex.z-dn.net/?f=%5Chat%7Bv%7D%20%3D%20%5Cfrac%7B%5Cvec%20v%7D%7B%5C%7C%5Cvec%20v%20%5C%7C%7D)
Where
is the norm of
, whose value can be found by Pythagorean Theorem.
Then, if
and
, then:
![\|\vec v\| =\sqrt{2^{2}+3^{3}}](https://tex.z-dn.net/?f=%5C%7C%5Cvec%20v%5C%7C%20%3D%5Csqrt%7B2%5E%7B2%7D%2B3%5E%7B3%7D%7D)
![\|\vec v\|=\sqrt{13}](https://tex.z-dn.net/?f=%5C%7C%5Cvec%20v%5C%7C%3D%5Csqrt%7B13%7D)
![\hat{v} = \frac{1}{\sqrt{13}} \cdot(2\,i + 3\,j)](https://tex.z-dn.net/?f=%5Chat%7Bv%7D%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B13%7D%7D%20%5Ccdot%282%5C%2Ci%20%2B%203%5C%2Cj%29)
![\hat{v} = \frac{2}{\sqrt{13}}\,i+ \frac{3}{\sqrt{13}}\,j](https://tex.z-dn.net/?f=%5Chat%7Bv%7D%20%3D%20%5Cfrac%7B2%7D%7B%5Csqrt%7B13%7D%7D%5C%2Ci%2B%20%5Cfrac%7B3%7D%7B%5Csqrt%7B13%7D%7D%5C%2Cj)
![\vec F \bullet \hat{v} = (0)\cdot \left(\frac{2}{\sqrt{13}} \right)+(-17)\cdot \left(\frac{3}{\sqrt{13}} \right)](https://tex.z-dn.net/?f=%5Cvec%20F%20%5Cbullet%20%5Chat%7Bv%7D%20%3D%20%280%29%5Ccdot%20%5Cleft%28%5Cfrac%7B2%7D%7B%5Csqrt%7B13%7D%7D%20%5Cright%29%2B%28-17%29%5Ccdot%20%5Cleft%28%5Cfrac%7B3%7D%7B%5Csqrt%7B13%7D%7D%20%5Cright%29)
![\vec F \bullet \hat{v} = -\frac{51}{\sqrt{13}}](https://tex.z-dn.net/?f=%5Cvec%20F%20%5Cbullet%20%5Chat%7Bv%7D%20%3D%20-%5Cfrac%7B51%7D%7B%5Csqrt%7B13%7D%7D)
![\vec F_{\parallel} = \left(-\frac{51}{\sqrt{13}} \right)\cdot \left(\frac{2}{\sqrt{13}}\,i+\frac{3}{\sqrt{13}}\,j \right)](https://tex.z-dn.net/?f=%5Cvec%20F_%7B%5Cparallel%7D%20%3D%20%5Cleft%28-%5Cfrac%7B51%7D%7B%5Csqrt%7B13%7D%7D%20%5Cright%29%5Ccdot%20%5Cleft%28%5Cfrac%7B2%7D%7B%5Csqrt%7B13%7D%7D%5C%2Ci%2B%5Cfrac%7B3%7D%7B%5Csqrt%7B13%7D%7D%5C%2Cj%20%20%5Cright%29)
(b) Parallel and perpendicular components are orthogonal to each other and the perpendicular component can be found by using the following vectorial subtraction:
![\vec F_{\perp} = \vec F - \vec F_{\parallel}](https://tex.z-dn.net/?f=%5Cvec%20F_%7B%5Cperp%7D%20%3D%20%5Cvec%20F%20-%20%5Cvec%20F_%7B%5Cparallel%7D)
Given that
and
, the component of
perpendicular to
is:
![\vec F_{\perp} = -17\,j -\left(-\frac{102}{13}\,i-\frac{153}{13}\,j \right)](https://tex.z-dn.net/?f=%5Cvec%20F_%7B%5Cperp%7D%20%3D%20-17%5C%2Cj%20-%5Cleft%28-%5Cfrac%7B102%7D%7B13%7D%5C%2Ci-%5Cfrac%7B153%7D%7B13%7D%5C%2Cj%20%20%5Cright%29)
![\vec F_{\perp} = \frac{102}{13}\,i + \left(\frac{153}{13}-17 \right)\,j](https://tex.z-dn.net/?f=%5Cvec%20F_%7B%5Cperp%7D%20%3D%20%5Cfrac%7B102%7D%7B13%7D%5C%2Ci%20%2B%20%5Cleft%28%5Cfrac%7B153%7D%7B13%7D-17%20%5Cright%29%5C%2Cj)
![\vec F_{\perp} = \frac{102}{13}\,i -\frac{68}{13}\,j](https://tex.z-dn.net/?f=%5Cvec%20F_%7B%5Cperp%7D%20%3D%20%5Cfrac%7B102%7D%7B13%7D%5C%2Ci%20-%5Cfrac%7B68%7D%7B13%7D%5C%2Cj)
(c) The work done by
through displacement
is:
![W = \vec F \bullet \vec v](https://tex.z-dn.net/?f=W%20%3D%20%5Cvec%20F%20%5Cbullet%20%5Cvec%20v)
![W = (0)\cdot (2)+(-17)\cdot (3)](https://tex.z-dn.net/?f=W%20%3D%20%280%29%5Ccdot%20%282%29%2B%28-17%29%5Ccdot%20%283%29)
![W = -51](https://tex.z-dn.net/?f=W%20%3D%20-51)
Atoms of the same element having unequal numbers of protons and electrons are called __________IONS