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Use the thermal power when applying nuclear fuel burnup. No capacity factor is supplied, so take a full-power year of $365$ days; if the operating fraction were $u$, the annual quantities in this part would be multiplied by $u$.The corresponding initial heavy-metal nuclear fuel requirement isAll nuclear fuel and concentrate masses below are uranium masses, excluding oxygen. Let $F,P,W$ denote uranium feed, product and enrichment tails, and $x_f,x_p,x_w$ the uranium-235 mass fractions. Conservation of total uranium and uranium-235 givessoWith $P=M$, the uranium oxide concentrate requirement is thereforeThis is not the gross mass of oxide concentrate. Both $F-P-W=0$ and $0.007F-0.050P-0.003W=0$ provide independent balance checks.

burnup refers to thermal energy per initial heavy-metal mass. Correct the electrical rating for thermal efficiency before using it, and apply the capacity factor once:Consequently the annual initial heavy-metal fuel requirement isLet $F,P,W$ be feed, enriched product and enrichment tails masses, all measured as uranium, and $x_f,x_p,x_w$ the corresponding uranium-235 mass fractions. The isotopic mass balance givesWith $P=M$, the uranium oxide concentrate requirement is thereforeThese are uranium or heavy-metal masses, not tonnes of uranium oxide. The check $327.394(0.007)=35.394(0.040)+292.000(0.003)$ closes the uranium-235 balance as well as the total mass balance.

Variability reduces firm capacity and creates balancing costs, but does not impose a universal tiny upper limit on the energy fraction from wind power. As an illustrative scale calculation, $10\mathrm{GW}$ installed at capacity factor $0.30$ produces $26.3\mathrm{TWh}$ annually, about $8.8\%$ of an assumed $300\mathrm{TWh}$ annual demand. Larger installations can supply larger fractions if the rest of the system is adapted.

Geographical spread, forecasting, interconnection, flexible generation, demand response and energy storage manage fluctuations on different timescales. They are not interchangeable: a battery that balances seconds does not necessarily cover a week of low wind. Correlated weather, curtailment, network constraints and reserve requirements become more important at high penetration. Backup capacity need not burn fuel continuously at the wind plant's nameplate output; energy and capacity should be accounted for separately. The defensible conclusion is that significant penetration requires system planning and has costs, not that variability alone confines wind to a negligible contribution.^[ref]

The judgement depends on the objectives and the replacement system, rather than following from a single technological fact. In the 2012 context, Germany had decided after Fukushima to accelerate its planned nuclear exit, with a timetable then extending to 2022. The contemporary official statement presented this as a reassessment of residual risk and a transition to efficiency and renewable supply.^[ref]

There is a serious climate opportunity cost if low-operational-carbon nuclear generation is replaced by unabated fossil generation. For example, replacing an illustrative $100\mathrm{TWh}\mathrm{yea}{\mathrm{r}}^{-1}$ with generation emitting $400$ or $900\mathrm{g}\mathrm{C}{\mathrm{O}}_2\mathrm{kW}{\mathrm{h}}^{-1}$ adds $40$ or $90$ million tonnes of carbon dioxide annually. Replacing that energy by wind at capacity factor $0.30$ would require about $38\mathrm{GW}$ of nameplate capacity, plus an adequate reliability plan; equal annual energy is not equal firm capacity.

Against continued operation must be weighed accident consequences, waste management, ageing, public preferences and the costs and feasibility of alternatives. Germany's specific risk assessment cannot be inferred solely from the different geography of Fukushima. A fast exit without credible low-carbon replacement can conflict with emissions goals; an exit supported by efficiency, infrastructure and low-carbon alternatives can pursue other legitimate objectives. Calling the decision intrinsically rational or irrational without those comparisons is not a technical conclusion. This answer evaluates the choice as posed in 2012, rather than importing later events as foreknowledge.

Tidal power offers predictable astronomical timing, while wave power can exploit an energetic marine resource. Neither is constant: tidal streams have slack-water periods, and wave energy varies with weather and season. Diversity can help a renewable portfolio, but resource size does not by itself establish economical extractable output.

For scale, a mean marine output of $5\mathrm{GW}$ would produce $43.8\mathrm{TWh}$ per year, about $15\%$ of an assumed $300\mathrm{TWh}$ annual electricity demand. Achieving that mean at capacity factor $0.30$ would require about $17\mathrm{GW}$ installed. This is an illustrative deployment requirement, not a measured UK resource estimate or a 2012 forecast. Tidal-stream kinetic power density scales as $\rho v^3/2$, making energetic sites valuable, but channel-wide extraction also changes the flow, so isolated-rotor power densities cannot simply be multiplied by sea area.

Harsh marine conditions, access for maintenance, survivability in storms, cable connections, navigation and ecological effects constrain deployment. Barrages additionally change estuaries and sediment transport. Research and demonstration may be worthwhile for energy diversity and industrial capability, but “important to investigate” is weaker than “indispensable at any cost”. Marine investment should be compared with efficiency and other low-carbon options using delivered energy, system value and environmental impacts.

“Never” cannot be established by one present price comparison. A useful comparison is levelized cost with common financing, capacity and system boundaries. For illustration, solar capital cost 1000 currency units/kW, annual capital-plus-maintenance charge 8%, and capacity factor 0.15 imply about 61 units/MWh. A coal plant with fuel, maintenance and capital costs of the same order is not separated by an immutable physical barrier. These are illustrative inputs, not current price quotations. Carbon costs and air pollution can worsen coal's comparison; intermittency, land and balancing costs can worsen solar's. Compare delivered services as well as panel-level energy. The defensible conclusion is contingent competition, not a universal impossibility.

The Shockley-Queisser calculation treats a single-junction solar cell with a single band gap, in steady state, with one collected electron-hole pair per absorbed above-gap photon, an ideal absorption edge, thermalized carriers and radiative recombination as the limiting recombination process. The source spectrum, cell temperature, angular acceptance and optical concentration must be specified. Below-gap photons are transmitted; energy above the gap is lost during carrier thermalization; the cell must emit photons by detailed balance, producing a recombination current and an entropy-related voltage loss. Delivering power at finite current also puts the operating voltage below the open-circuit voltage. Nonradiative recombination, resistance and imperfect collection worsen a real cell but are not required for the ideal limit.

Three ways to change those assumptions are tandem solar cells, which divide the spectrum among gaps and reduce both transmission and thermalization losses; hot-carrier solar cells, which aims to collect excess carrier energy before thermalization; and carrier multiplication or spectral conversion, which aims to use a high-energy photon for more than one excitation or combine otherwise unusable sub-gap photons. These concepts have additional practical losses and do not automatically outperform an optimized conventional device. The usual unconcentrated single-junction optimum is approximately one third under a terrestrial solar spectrum, rather than a universal efficiency independent of illumination.

For the geometrical estimate, take the stated horizontal equinox irradiance to set a constant direct-normal reference. The equinox solar-noon elevation is ${\alpha }_e=90^{\circ }-51.75^{\circ }=38.25^{\circ }$, so this reference is $I_n=1/\sin {\alpha }_e\simeq 1.62\mathrm{kW}{\mathrm{m}}^{-2}$. A south-facing panel with tilt $\beta =41.1^{\circ }$ has noon incidence factor $\cos (51.75^{\circ }-\delta -41.1^{\circ })$, where $\delta =\pm 23.44^{\circ }$. Relative to the $1\mathrm{kW}{\mathrm{m}}^{-2}$ plane-of-array rating,These are the results of that idealized geometrical normalization, not credible seasonal production forecasts. Its inferred direct-normal irradiance already exceeds the approximately $1.36\mathrm{kW}{\mathrm{m}}^{-2}$ solar irradiance outside the atmosphere, so the supplied horizontal benchmark cannot describe a purely direct noon beam literally. Real direct and diffuse fractions, atmospheric attenuation at low winter elevation, cell temperature and inverter clipping are unspecified. An alternative assumption of $1\mathrm{kW}{\mathrm{m}}^{-2}$ direct-normal irradiance gives approximately $4.88$ and $4.14$ kW. A physically unique maximum cannot be inferred without an irradiance model.

The stated annual output corresponds to $4100/5=820$ full-rated hours, an average power of $0.468$ kW and a capacity factor of $9.4\%$. Night, cloud, seasonal day length and other losses explain the large difference from an instantaneous sunlit estimate.

For a national scale estimate, take UK area $2.44\times 10^{11}{\mathrm{m}}^2$, population $6.6\times 10^7$, and annual mean solar input $100\mathrm{W}{\mathrm{m}}^{-2}$. Covering five percent with twenty-percent-efficient modules givesThis is comparable with an order-$100$ kWh daily per-person primary-energy budget, and much larger than electricity use alone, of order $10$-$15$ kWh per person per day. It is a gross area-and-flux estimate: access land, shading, seasonal storage, curtailment and conversion between primary energy and electrical end use all affect its interpretation.

Distributed generation changes the shape of infrastructure rather than eliminating it. A $1$ GW power station is large, but supplying a national mean demand of tens of gigawatts from smaller intermittent generators still requires transmission, distribution, power conversion, forecasting, balancing and often storage or dispatchable reserve. Geographic diversity can reduce weather correlations only if power can move between regions.

For scale, delivering $30$ GW through a network is a continuous transfer of $30$ billion joules each second. Even a distributed average installation of $3$ kW per household needs ten million participating households to reach that power, before allowing for capacity factor. Solar roofs can reduce some local flows while export peaks or winter deficits increase others. District heat, offshore wind connections, interconnectors and fuel transport also have economies of scale.

Large centralized assets can introduce single-point failure, slow construction and financing risk; modular systems can be installed incrementally and offer local control. Conversely, network reinforcement and seasonal adequacy cannot be inferred from the size of an individual panel. A defensible conclusion is that an effective mix may combine small generators with large shared infrastructure. The categorical claim that large-scale infrastructure has become obsolete does not follow from the existence of distributed generation.

Conversion of atmospheric kinetic energy into useful power, commonly by turbines driving generators. Annual energy equals nameplate capacity times capacity factor times elapsed time, while the contribution to reliable peak supply is a separate system property. Weather correlation, transmission, flexibility and curtailment affect large-scale integration.