GATE CY 2026 Question Paper (07-Feb-2026) (Shift 2)

The positions of two atoms in spherical polar coordinates ($r,\theta ,\Phi$) are ($1,\frac{\pi }{2},\frac{\pi }{2}$) and ($1,\frac{\pi }{4},\frac{3\pi }{2}$), where the distance is in Å and the angles are in radian. The interatomic distance (in Å) is ______ (rounded off to two decimal places).

If the translational partition function for H${}_2$ confined in a 1 L vessel at 300 K is $y\times 10^{27}$, then the value of $y$ is ______ (rounded off to one decimal place).
(Given: Atomic mass (in amu): H = 1.008; 1 amu = $1.661\times 10^{-27}$ kg; $h=6.626\times 10^{-34}$ J s; $k=1.381\times 10^{-23}$ J K${}^{-1}$)

In a calibrated pH meter comprising of glass electrode-standard calomel electrode, the potential for a buffer solution of pH 4.01 is measured as 0.814 V at 25 ${}^{\circ }$ C. For a $4.0\times 10^{-3}$ M solution of acetic acid, the measured potential (in V) is ______ (rounded off to three decimal places).
(Given: $K_a$ of acetic acid at 25 ${}^{\circ }$ C = $1.75\times 10^{-5}$; $2.303RT/F=0.059$; Assume: $a_{H^{+}}=[H^{+}]$)

The Brunauer-Emmett-Teller (BET) surface area measurement data for adsorption of N${}_2$ gas at 77 K on 1.0 g of an adsorbent fits into a straight line, when $\frac{z}{(1-z)V}$ is plotted against $z$. The slope and intercept of the straight line are $6\times 10^{-4}$ mm${}^{-3}$ and $4\times 10^{-6}$ mm${}^{-3}$, respectively. The surface area (in m${}^2$ g${}^{-1}$) of the adsorbent is ______ (rounded off to one decimal place).
(Given: 1 mm${}^3$ of N${}_2$ gas corresponds to $2.7\times 10^{16}$ molecules and each molecule occupies 0.16 nm${}^2$. $V$ is the volume of gas adsorbed in mm${}^3$, $z$ is $p/p_o$, where $p$ is the pressure of the N${}_2$ gas and $p_o$ is equilibrium vapour pressure of liquid N${}_2$)

The orbital angular momentum (L) of an electron is $\sqrt{12}\hslash$. The minimum angle between L and its z-component (in degrees) is ______ (rounded off to one decimal place).