Light of wavelength $4000 \, \mathring A$ is incident on a sodium surface for which the threshold wavelength of photoelectrons is $5420 \, \mathring A$. The work function of sodium is .......... $eV$.

Three waves of equal frequency having amplitudes $10 \mu m,$ $4 \mu m,$ and $7 \mu m$ arrive at a given point with a successive phase difference of $\frac{\pi}{2}.$ The amplitude of the resulting wave in $\mu m$ is given by

When an object is placed at a distance of $25 \, cm$ from a concave mirror,the magnification is $m_1$. The object is moved $15 \, cm$ farther away with respect to the earlier position,and the magnification becomes $m_2$. If $m_1/m_2 = 4$,the focal length of the mirror is $..... \, cm$ (Assume image is real,$m_1$ and $m_2$ are numerical values).

For the electrochemical cell, $Mg ( s )\left| Mg ^{2+}( aq , 1 M ) \| Cu ^{2+}( aq , 1 M )\right| Cu ( s )$ the standard emf of the cell is $2.70 V$ at $300 K$. When the concentration of $Mg ^{2+}$ is changed to $x M$, the cell potential changes to $2.67 V$ at $300 K$. The value of $x$ is.

(given, $\frac{ F }{ R }=11500 K V ^{-1}$, where $F$ is the Faraday constant and $R$ is the gas constant, The value of $\ln (10)=2.30$ )

The activity of a radioactive sample is measured as $N_0$ counts per minute at $t = 0$ and $N_0/e$ counts per minute at $t = 5$ minutes. The time (in minutes) at which the activity reduces to half its value is

The equation $8 x^2-24 x y+18 y^2-6 x+9 y-5=0$ represents a