The electronic configuration of a metal $M$ is $1s^2 \, 2s^2 \, 2p^6 \, 3s^1$. What will be the formula of its oxide?

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U(x) = \frac{a}{x^{12}} - \frac{b}{x^6}$,where $a$ and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D = [U(x = \infty) - U_{\text{equilibrium}}]$,what is the value of $D$?

The objective and eyepiece of an astronomical telescope are double convex lenses with refractive index $1.5$. When the telescope is adjusted to infinity,the separation between the two lenses is $16 ~cm$. If the space between the lenses is now filled with water (refractive index $4/3$) and the telescope is again adjusted for infinity,then the present separation between the lenses is: (in $~cm$)

$v_1$ is the frequency of the series limit of the Lyman series,$v_2$ is the frequency of the first line of the Lyman series,and $v_3$ is the frequency of the series limit of the Balmer series. Then:

The radius of the circle with the polar equation $r^2-8r(\sqrt{3}\cos\theta+\sin\theta)+15=0$ is

If $y = mx + c$ is a tangent to the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$,then the value of $c$ is