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Ionic radii of cations is smaller than anions, also more the positive charge less be the ionic radii and more the negative charge more be the ionic radii. Hence correct order of ionic radii is, $p^{3-}>S^{2-}>C{l}^{-}>K^{+}>C{a}^{2+}$

$dM=\sqrt[]{2R{h}_T}+\sqrt[]{2R{h}_R}$

$?h_T+h_R=160$

[Given]

So, hR = 160 - hT

$d_M=\sqrt[]{2R{h}_T}+\sqrt[]{2R\left(160-h_T\right)}$

$\therefore d_M=\sqrt[]{2\times 6400000\times 80}+\sqrt[]{2\times 6400000\times 80}$

$=2\times 4\times 8\times 10^3$

dM = 64 km

When red phosphorus is heated in a sealed tube at 803 K, a - black phosphorus is formed.

Currently, CSU Long Beach has a total student strength of 39,858 enrolled on its campus, of which 35,843 are UG and 4,015 are PG. The enrollment trends for California State University Long Beach for the last five years are given below: 

$A{g}^{+}\left(aq\right)+2N{H}_3\left(aq\right)?Ag{\left(N{H}_3\right)}_2^{+}\left(aq\right)$

t = 00.8 M $\left(\frac{a}{2}\right)M$                  

0 $=\infty$   5 × 10^-8 M   $\left(\frac{a}{2}-1.6\right)M$   0.8M

$k_f=\frac{\left[Ag{\left(N{H}_3\right)}_2^{+}\right]}{\left[A{g}^{+}\right]{\left[N{H}_3\right]}^2}$

$10^8=\frac{0.8}{\left(5\times 10^{-8}\right){\left(\frac{a}{2}-1.6\right)}^2}$

$\frac{a}{2}=2$

 Concentration of NH₃ added =   $\frac{a}{2}=2M$

 Volume of solution = 2L

 Moles of NH₃ added = 2 × 2 mol = 4 mol.

E = (50 N/s) sin (t – x/c)

Energy 5.5 × 10^-12 J., vol v =?

$u=\frac{1}{2}{\epsilon }_0{E}^2\to$ energy density

$?u=\frac{U}{v}\Rightarrow U=uv$

= $\frac{1}{2}{\epsilon }_0{E}^2.v$

$v=\frac{5.5\times 10^{-12}\times 2}{8.55\times 2500\times 10^{-12}}\times 10^{6}c{m}^3$

= 497

$\cong 500c{m}^3$

Transverse waves can travel through solids or any medium that can withstand shearing strain. Fluids, including liquids and gases, cannot sustain shear force, so such types of mechanical waves cannot travel through them. 

Longitudinal waves can travel through all elastic media that can sustain compressive strain. That means, these mechanical waves can travel through solids, liquids, and gases.  

(a) $Calamine:ZnC{O}_3$  

(b) Malachite : $CuC{O}_3.Cu{\left(OH\right)}_2$  

(c) Siderite : FeCO₃

(d) Sphalerite : ZnS

Millimoles of HCl = 200 × 0.2 = 40

Millimoles of NaOH = 300 × 0.1 = 30

Heat released =  $\frac{30}{1000}\times 57.1\times 1000J=1713J$

$\left[\begin{array}{l}\rho =\frac{m}{v}\\ m=\rho v\end{array}\right]$

Mass of solution = 500 × 1 g

= 500 g

Specific heat of water = 4.18 Jg^-1 K^-1

$\Delta T=\frac{q}{mc}$

$=\frac{1713}{500\times 4.18}°C$  

$=81.96\times 10^{-2}°C\approx 82\times 10^{-2}°C$

Ans. = 82

$?\frac{P_i=P_f}{m\times 40}=\frac{m}{2}v\text{'}+\frac{m}{2}\times 60$

v’ = 20 m/s

$K{E}_f=\frac{1}{2}\frac{m}{2}\left[v^2+60^2\right]$

$K{E}_f=\frac{1}{2}\frac{m}{2}\left[v^2+60^2\right]$

$\frac{\Delta KE}{KE}=\frac{\frac{1}{2}m\left(2000\right)-\frac{1}{2}m\left(1600\right)}{\frac{1}{2}m\left(1600\right)}$

$\therefore x=1$

Let molarity of KMnO₄ = x

$KMn{O}_4+FeS{O}_4\to F{e}_2{\left(S{O}_4\right)}_3+M{n}^{2+}$

n = 5         n = 1         Ferric sulphate

equivalent of KMnO₄ = equivalent of FeSO₄

5 × x × 10 = 1 × 0.1 × 10

x = 0.02 M

Strength = (0.02 × 158) = 3.16g/L

= 316 × 10^-2 g/L

Ans. = 316

$\underset{\left(z=93\right)}{Np}\Rightarrow 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^{10}4p^{6}5s^2$

$4d^{10}5p^{6}6s^{2}4f^{14}5d^{10}6p^{6}7s^{2}5f^{4}6d^1$

Total number of f-electrons = 14 + 4 = 18 electrons

Ans. = 18

$x=Asin\omega t$   (Eq. of a particle executing SHM)

When KE = PE

$\frac{1}{2}m{v}^2=\frac{1}{2}k{x}^2$

$\frac{1}{2}m{\omega }^2\left(A^2-x^2\right)=\frac{1}{2}k{x}^2\left[?k=m{\omega }^2\right]$

A2 – x2 = x2

 $So,\frac{A}{\sqrt[]{2}}=Asin\omega t$

$\frac{1}{\sqrt[]{2}}=sin\omega t$

$\therefore t=\frac{T}{8}$

The estimated 2025-26 Gannon University Cost of Attendance can be found out from the table given below:

Sound waves and water waves are mechanical waves, which always require a medium to travel. Light, however, does not require a medium to propagate, as it is electromagnetic.  Light can travel through vacuum, while sound and water waves cannot travel through vacuum.