About how long would it take for a (full) can of beer at room temperature to topple over spontaneously, as a result of quantum tunneling? Treat it as a uniform cylinder of mass m, radius R, and height h. As the can tips, let x be the height of the center above its equilibrium position (h/2). The potential energy is mgx, and it topples when x reaches the critical value Calculate the tunneling probability (Equation 9.23), for E = 0. Use Equation 9.29, with the thermal energy ((1/2) mv² = (1/2) k_B T to estimate the velocity. Put in reasonable numbers, and give your final answer in years.

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X0 = XO R² + (h/2)²-h/2.